Patent Publication Number: US-2021171173-A1

Title: Personal watercraft

Description:
TECHNICAL FIELD 
     The field of this invention generally relates to personal watercraft. 
     BACKGROUND 
     Pelican International Inc. manufactures paddle boats. Companies which provide linear guides include Igus, Hiwin, VBX and Thomson. Neither a standard stand-up paddle board nor a Hobie® Eclipse board with MirageDrive allows a rider to generate thrust by sliding their feet forward and rearward. The Hobie Eclipse does not provide separate flotation devices for each foot. The MirageDrive does not attach to a standard stand up paddle board. 
     SUMMARY OF THE INVENTION 
     The subject invention provides a personal watercraft which typically includes a floatation member for supporting a rider, typically supported entirely out of the water; although a portion of the rider may be supported in the water. Throughout this patent application, reference will be made to water, typically fresh or salt water; however, the provided watercraft is not intended to be limited to use in water, since it will work as described within many different fluids. The watercraft typically also includes a thrust assembly, and may include a steering assembly and a braking assembly. The assemblies may be actuated either mechanically or electrically. The thrust assembly is typically human powered; although, it may also be solar powered, electric powered, or wind powered. The thrust, steering, and braking assemblies may be added after-market to an existing stand-up paddle board (SUP), i.e., retrofit, or built into one or a plurality of SUPs during initial manufacturing. Throughout this application, the thrust, steering, or braking controlling and actuating assemblies provided by one embodiment may be readily combined with, used with, or substituted for, another embodiment. For example, for clarity of the drawings, a simplified embodiment might show a thrust control and actuation assembly, but not show a steering or braking control or actuation assembly; however, any steering or braking control or actuation assembly provided by another embodiment may be combined with, used with, or substituted for, such simplified embodiment as if the braking control or actuation assembly were explicitly provided in the simplified embodiment. Throughout this application, the term SUP includes, but is not limited to, a stand-up paddle board, surf board, kayak, canoe, pontoon, or any of a variety of buoyant objects, boards, boats, inflatable devices, and the like, or any other functionally similar floatation or buoyant apparatus, where the apparatus may comprise a plurality of floatation or buoyant members, and where the apparatus is capable of providing buoyancy support for at least one user or rider in a fluid, which may be water. When a plurality of SUPs are used by a single rider, each SUP is typically more narrow than usual, so the rider&#39;s feet are not unreasonably far apart. When the thrust assembly is human powered, it is typically leg or arm powered. When the thrust assembly is leg powered, typically the legs can move backward and forward in a sliding motion (like cross-country skiing), up and down in a stomping fashion (like marching in place), or move in a loop trajectory (such as on an Elliptical machine). When the thrust assembly is arm powered, typically the rider&#39;s arms may move forward and backward, and move either together or separately. The thrust assembly may combine leg and arm powered assemblies. The thrust assembly may include one or a plurality of paddles or flippers that typically are positioned to the side of the SUP or under the SUP. In some cases the terms thrust fin and thrust paddles are used interchangeably. In some cases, the terms foot support, foot holder, carriage, platform, pedal, and pad are used interchangeably. In some drawings to aid understanding, part of the drawing is provided in a perspective view while the rest is provided in a non-perspective view. 
     Although the watercraft is designed for use in fresh water or salt water, the watercraft may be used in any convenient fluid. 
     When the thrust assembly is leg powered, the thrust assembly may include one or more guides, such as linear guides that have carriages for sliding on them. Typically the carriages may have supports, which may removably secure a rider&#39;s feet. Typically two linear guides are positioned to a SUP, one linear guide on the right side, and one linear guide on the left side, and each linear guide having a carriage, one carriage for each of the rider&#39;s feet. Typically handlebars are attached to the SUP, where the rider may push against the handlebars in order to translate one or both of the carriages rearward. Movement of a carriage rearward typically causes a paddle, such as a paddle blade, to move rearward to generate forward thrust of the SUP. Movement of a carriage may also cause a flexible or rotatable flipper to move up and down to generate forward thrust of the SUP. Typically, forward movement of a carriage is substantially resistance free for a “recovery phase,” for instance where the paddle may recover out of the water, or turn relative to the water and direction of motion so that resistance is reduced while the paddle moves through the water. 
     A benefit of a rider sliding their feet on carriages which may be associated with linear guides is that certain muscles may be targeted for exercise. For instance, when a rider slides their foot rearward to generate forward thrust of their watercraft, such as an SUP, they might exercise their gluteus maximus, their hamstrings, their lower back muscles, and other core muscles. Such muscles might not receive the same level of exercise as when other movement of the feet are used to generate thrust, such as when the feet use a stomping motion, such as up and down. That is, a cross-country skier which slides on their skis uses different muscles than a walker and a bicycle rider. 
     Another benefit of a rider sliding their feet on carriages which may be associated with linear guides is the gliding feeling they perceive, which is related to the gliding feeling a cross-country skier feels. Cross-country skiers may prefer cross-country skiing over running due to the enjoyable gliding sensation. 
     Other movements of the rider&#39;s feet may be substantially resistance free, such as when lifting a foot that is controlling a flipper, the flipper may rotate to reduce resistance. 
     A first useful embodiment provides a thrust assembly having a guide for attachment to a buoyant member, such as an SUP, the guide having a support for supporting a human foot and for guiding movement of a human foot forward and rearward. The embodiment has a paddle for propelling the buoyant member forward when the rider uses their foot to force the support rearward relative to said buoyant member. 
     The first useful embodiment may also have two sub-assemblies each having the support, the guide, and the paddle, wherein one of the sub-assemblies is for positioning on the left side and one of the sub-assemblies is for positioning on the right side of the buoyant member. 
     A second useful embodiment may also have two thrust assemblies each having a support and a thrust member for applying force against water, wherein one of the thrust assemblies is for positioning on a left buoyant member and one of said thrust assemblies is for positioning on a right buoyant member, wherein a rider is capable of placing their left foot on the support on the left buoyant member and placing their right foot on the support on the right buoyant member and moving their right and left feet forward and rearward relative to each other, whereby each of the buoyant members moves forward in water. 
     A guide of the second useful embodiment may comprise a linear guide, and each of the supports may comprise an attachment for releasably securing a human foot to the support. 
     A third useful embodiment of the subject invention is a personal watercraft comprising a buoyant member, a guide attached to the buoyant member, the guide having a support for supporting a human foot and for guiding movement of a human foot forward and rearward, and a paddle for propelling the buoyant member forward when the support moves rearward relative to the buoyant member. 
     The third useful embodiment may comprise a buoyant member, two guides attached to the buoyant member, each of the guides having a support for supporting a human foot and for guiding movement of a human foot forward and rearward, and a paddle associated with each the supports for propelling the buoyant member forward when one of the supports moves rearward relative to the buoyant member. 
     A fourth useful embodiment includes solar cells to power an electric thrust system, such as an electric motor with a propeller, a paddle, a paddle wheel, a flipper, and the like. 
     Each of the guides of an embodiment may comprise a linear guide, and each of the supports may comprise an attachment for releasably securing a human foot to the support. 
     A first useful technique provided by the subject invention comprises a guide attached to a buoyant member, the guide having a support for supporting a human foot and for guiding movement of a human foot forward and rearward, and a paddle for propelling the buoyant member forward when the support moves rearward relative to the buoyant member, where the technique includes sliding a foot rearward propelling the buoyant member forward, and sliding the foot forward to move the paddle forward. 
     A second useful technique provided by the subject invention comprises a support for supporting a human foot, and a flipper for propelling the buoyant member forward when the support moves toward the buoyant member. The technique includes pushing a foot downward toward the buoyant member, and the flipper moving away from the buoyant member to deeper water propelling the buoyant member forward. 
     The second useful technique may include lifting afoot upward away from the buoyant member, and the flipper moving toward the buoyant member to shallower water propelling the buoyant member forward. 
     The second useful technique may include pushing a foot downward toward the buoyant member causing a second foot to lift upward away from the buoyant member. 
     Handlebars on an SUP may be released to slide through a hole in the SUP to lower the center of gravity to make the SUP more stable and less prone to turning over if a rider wants to get onto the SUP from the water. For instance, there may be a knob on or near the handlebars to release it so it may slide down. 
     When an electric motor is used, such as a trolling motor, handlebars may have a battery gauge indicating the amount of electrical power being used and how much is left in a battery. Alternatively, LEDs may be used, such as green, yellow, and red LEDs, to indicate battery level. 
     When a trolling motor is used, the trolling motor may be attached to the water side of the handlebars, and it may be retractable all the way up into the body of the SUP so the SUP may be dragged on sand and dirt without damaging the trolling motor. An extensible paddle may be slid into and out of a storage slot on the SUP, or in the handlebars, in case the battery dies. 
     The SUP may have a kick stand with retractable wheels so the rider may conveniently roll the SUP to the water&#39;s edge. Once the SUP is placed in the water, the wheels may be removed, or retracted into the body of the SUP to prevent drag. Alternatively, the wheels may be rotated up and above the surface of the water, and may remain to the side of the SUP. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIGS. 1-62  provide embodiments of various personal watercraft, associated assemblies, sub-assemblies, members, elements, and components. 
         FIG. 1A  is a side view of a first useful embodiment of the subject invention comprising a linear sliding assembly in a forward position and attached to a standup paddle board (SUP). 
         FIG. 1B  is a rear end view of the embodiment of  FIG. 1A , where the linear rail of the linear sliding assembly is shown as part of the SUP. 
         FIG. 1C  is a side view of the embodiment of  FIG. 1A , where the linear sliding assembly in a rear position. 
         FIG. 1D  is a rear end view of the embodiment of  FIG. 1C , where the linear rail of the linear sliding assembly is shown as part of the SUP. 
         FIGS. 2A-2C  provide alternative embodiments of the sector  108  that rotates the worm gear  112  in  FIGS. 1A-1D . 
         FIGS. 3A-3C  provide rear-end cross-sections of carriage-paddle assemblies.  FIGS. 3D-3G  are plan views of the right carriage  300  of  FIG. 3C  in different positions along a linear guide  301 .  FIG. 3H  is a side view of the right carriage  300  in the position shown in  FIG. 3G . 
         FIGS. 4A-4D  provide steering and braking assemblies. 
         FIG. 5A  is a perspective view of a useful embodiment of the invention.  FIG. 5B  is a perspective view that provides exemplary embodiments for cams, gears, or wheels that control the position of paddle blades.  FIG. 5C  provides a perspective view of the exemplary embodiment of  FIG. 5B  in a second state.  FIG. 5D  provides an illustrative embodiment of a fastener assembly for securing the removable mounting structure into a cavity in the SUP. 
         FIG. 5E  provides a side view of a low-profile strap positioned against the surface of the SUP in the water. 
         FIG. 6  is a perspective view of a useful embodiment of the invention. 
         FIGS. 7A, 7B, and 7C  provide a side view, perspective view, and top view, respectively, of an illustrative embodiment of an SUP comprising one or more flippers to provide forward thrust. 
         FIGS. 8A and 8B  provide perspective views of a flipper with a connected end and a free end. 
         FIG. 9A  is a perspective view of an illustrative embodiment of a plurality of SUP members, each comprising one or more thrust actuators for providing forward thrust.  FIG. 9B  is a perspective view of a thrust actuator, such as may be used in  FIG. 9A .  FIG. 9C  is a perspective view of the collapsed thrust actuator of  FIG. 9B .  FIG. 9D  is an end view of a partially collapsed thrust actuator.  FIG. 9E  is a perspective view of means for securing a foot to a foot support.  FIG. 9F  is a side view of the apparatus of  FIG. 9E , where the rider has lifted their heel, such as when pushing rearward.  FIG. 9G  is a top view of a steering control and actuator assembly.  FIG. 9H  is a front end view of one embodiment of SUPs, where the curvature of the bottoms of the SUPs are substantially symmetrically curved.  FIG. 9I  is a front end view of another embodiment of SUPs, where the curvature of the bottoms of the SUPs are not symmetrically curved.  FIG. 9J  is a side view of one exemplary front end of the SUPs, showing an exemplary fluid/water level. 
         FIGS. 10A-10B  are a side view of a useful embodiment of a thrust assembly.  FIGS. 10C-10D  are a side view of a useful embodiment of another thrust assembly. 
         FIGS. 11A-11B  are a side view of a useful embodiment of another thrust assembly. 
         FIGS. 11C-11D  are a side view of a useful embodiment of another thrust assembly. 
         FIGS. 12A-12B  are a side view of a useful embodiment of another thrust assembly. 
         FIGS. 12C-12D  are a side view of a useful embodiment of another thrust assembly. 
         FIG. 13A  is a side view of a useful embodiment of another thrust assembly.  FIG. 13B  provides one exemplary embodiment of a rotation-direction-limiting structure that is positioned in functional relation to each thrust paddle wheel. 
         FIG. 14A  is a top view of a solar-powered SUP in water.  FIG. 14B  is a side view of the solar-powered SUP of  FIG. 14A . 
         FIG. 15A  is a side view of a useful embodiment of another thrust assembly.  FIG. 15B  provides thrust paddles in a retracted position. 
         FIG. 16  is a top view of an exemplary apparatus that prevents a plurality of SUPs from coming into contact with each other, and allows the SUPs to move uninhibited in a substantially parallel direction relative to each other along a desired direction of travel. 
         FIG. 17  is a top view of an exemplary apparatus that protects a plurality of SUPs when they contact each other. 
         FIG. 18A  is a prospective view of a floatation apparatus.  FIG. 18B  is a perspective view of a foot holder. 
         FIG. 19A  is a side view of a useful embodiment of another thrust assembly.  FIG. 19B  is a plan view of two SUPs according to  FIG. 19A .  FIG. 19C  is a rear-end view of the SUPs shown as connected in  FIG. 19B .  FIG. 19D  is a side view of a useful embodiment of another thrust assembly. 
         FIG. 20A  is a side view of a useful embodiment of another thrust assembly.  FIG. 20B  is a side view of a useful embodiment of another thrust assembly similar in structure to  FIG. 20A , except the foot carriage includes a linear bearing.  FIG. 20C  is a rear-end view of the thrust assembly of  FIG. 20B . 
         FIG. 21A  is a plan view of a useful embodiment of another thrust assembly.  FIG. 21B  is a side view of the thrust assembly of  FIG. 21A .  FIG. 21C  is a side view, where the thrust paddles on the circulatory belt in  FIG. 21B  are substituted with collapsible thrust actuators.  FIG. 21D  is a side view, where the pulleys and belt of  FIG. 21A  that mechanically connects the treadmill control input with the circulatory belt output is replaced by fixed gears.  FIG. 21E  is an end view, where the fixed gears of  FIG. 21D  are replaced by a gear box. 
         FIG. 22A  is a rear-end view of the thrust assembly of  FIG. 22B , where  FIG. 22B  is a side view of a useful embodiment of another thrust assembly. 
         FIGS. 23A-23D  provide a wireless steering apparatus. 
         FIG. 24A  is a perspective view of a thrust paddle with a curved paddle edge.  FIG. 24B  is a cross section of the thrust paddle near the curved paddle edge.  FIG. 24C  is a cross section of the thrust paddle midway between the curved paddle edge and the straight edge. 
         FIG. 24D  is a cross section of the thrust paddle near the straight edge. 
         FIG. 25A  is a rear-end view of the thrust assembly of  FIG. 25B , where  FIG. 25B  is a side view of a useful embodiment of another thrust assembly. 
         FIG. 26A  is a rear-end view of the thrust assembly of  FIG. 26B , where  FIG. 26B  is a side view of a useful embodiment of another thrust assembly. 
         FIG. 27.1  is a side view of a useful embodiment of another thrust assembly where the rider may stand sideways on the SUP.  FIG. 27.2  is a side view of a useful embodiment of another thrust assembly where the rider may stand sideways on the SUP. The foot support may be connected to flippers by a Mirage Drive, such as is part of a Hobie Mirage Eclipse.  FIG. 27.3 a    is a plan view of the useful embodiment of another thrust assembly where the rider may stand sideways on the SUP.  FIG. 27.3 b    is a front-end view of the useful embodiment of another thrust assembly where the rider may stand sideways on the SUP. 
         FIGS. 28A-28C  are a side views of useful embodiments of other thrust assemblies.  FIG. 28D  is a plan view, and  FIG. 28E  is a front-end view, of the useful embodiment of  FIG. 28A . 
         FIG. 29.3 c    is a side view of a useful embodiment of another thrust assembly.  FIG. 29.3 d    is a plan view of a useful embodiment where a throttle grip comprises a Bowden cable to control the rudder.  FIG. 29.4 a    is a side view of a useful embodiment of another thrust assembly.  FIG. 29.4 b    is a front-end view of a useful embodiment where the two foot supports are kept 180 degrees out of phase using a pulley and pulley cable. 
         FIG. 30.5 a    is a perspective view of a useful embodiment of another thrust assembly.  FIG. 30.5 b    provides an assembly comprising pulleys and a pulley belt to keep the two handles 180 degrees out of phase.  FIG. 30.6 a    is a side view of a useful embodiment of another thrust assembly.  FIG. 30.6 b    is similar to  30 . 6   a , except the hand lever is connected to the curved rod using a tie rod with rotary joints on each end.  FIG. 30.7  is a plan view of a useful embodiment of another thrust assembly. 
         FIG. 31.8 a    is a side view of a useful embodiment of another thrust assembly, where the up and down motion of the foot support is constrained by a four-bar mechanism.  FIG. 31.8 b    is a front-end view of a useful embodiment, such as a portion of the embodiment of  FIG. 31.8 a   .  FIG. 31.9  is a side view of a useful embodiment of another thrust assembly.  FIG. 31.10 a    is a front view of a useful embodiment for keeping the right and left foot supports moving 180 degrees out of phase.  FIG. 31.10 b    is a side view of the flexible flipper of  FIG. 31.10 a   .  FIG. 31.10 c    is a front view of a useful embodiment for keeping the right and left foot supports moving 180 degrees out of phase.  FIG. 31.11  is a side view of a useful embodiment of another thrust assembly, where handle levers may be connected to the flippers by a Mirage Drive, such as is part of a Hobie Mirage Eclipse. 
         FIG. 32  is a side view of a useful embodiment of another thrust assembly. 
         FIG. 33.1  is a side view of a useful embodiment of another thrust assembly.  FIG. 33.2  is a side view of a useful embodiment of another thrust assembly.  FIG. 33.3  is a side view of a useful embodiment of another thrust assembly. 
         FIGS. 34A-34C  are a side views of useful embodiments of other thrust assemblies.  FIG. 34D  is a plan view of the useful embodiment of  FIG. 34C .  FIGS. 34E-34F  are a side views of useful embodiments of other thrust assemblies.  FIG. 34G  is a side view of the useful embodiment of  FIG. 34F  where the handlebars are folded down against the SUP. 
         FIGS. 35A-35B  are a side views of useful embodiments of other thrust assemblies.  FIG. 35C  is a plan view of a useful embodiment of another thrust assembly.  FIG. 35D  is a side/perspective view of the useful embodiment of  FIG. 35C . 
         FIG. 36A  is a plan view of a useful embodiment of another thrust assembly.  FIG. 36B  is a plan/side view of the useful embodiment of  FIG. 36A .  FIGS. 36C-36F  are different views of a motor housing with a flexible fin for propulsion. 
         FIG. 37A  is a perspective view of a useful embodiment of another thrust assembly, where a left foot support and a right foot support are guided by linear bearings on an SUP.  FIG. 37B  is an end view of a useful embodiment of another thrust assembly, where the left and right propulsion fins are positioned to the side of the SUP.  FIG. 37C  is an end view of an alternate to the useful embodiment of  FIG. 37B , where the left and right propulsion fins are positioned underneath the SUP.  FIGS. 37D-37E  are side views of useful embodiments of a foot support.  FIG. 37F  is a plan view of the useful embodiment of the foot support of  FIG. 37E .  FIG. 37G  is a side view of the useful embodiment of the foot support of  FIG. 37E .  FIG. 37H  is a side view of a useful embodiment of a foot support. 
         FIG. 38A  is a perspective view of a useful embodiment of another thrust assembly, where a portion of the rider is positioned below the water level.  FIG. 38B  is a plan view of the useful embodiment of  FIG. 38A . 
         FIGS. 39A-39B  are side views of useful embodiments of other thrust assemblies, where the rider faces to the side of the SUP.  FIG. 39C  is an end view of the useful embodiment of  FIG. 39B .  FIG. 39D  is a plan view of the flexible flipper of the useful embodiment of  FIG. 39B , and  FIG. 39E  is a plan view of the flexible flipper of the useful embodiment of  FIG. 39A .  FIGS. 39F-39G  are plan views of useful embodiments of the turning structure of  FIG. 39A  that use a Bowden cable.  FIG. 39H  is a combination side/perspective view of a useful braking embodiment comprising a brake lever and a Bowden cable.  FIG. 39I  is a perspective view of a useful embodiment of another thrust assembly, where the left and right foot supports are constrained by a constraint assembly to rotate in opposite directions. 
         FIG. 40A  is a side view of a useful embodiment for wirelessly controlling a rudder of an SUP.  FIG. 40B  is a side view of a useful embodiment for remotely mechanically controlling a rudder of an SUP. 
         FIGS. 41A-41B  are side views of useful embodiments of other thrust assemblies, where thrust is provided by a paddle wheel which may be located to the rear or side of an SUP.  FIG. 41C  is a plan view of a useful embodiment of a thrust assembly comprising one or more paddle wheels for providing thrust. 
         FIG. 42A  is a side view of a useful embodiment of another thrust assembly, where a drive sprocket is connected to a rear sprocket.  FIG. 42B  is a side view of a useful embodiment of a braking assembly, where the heel of a rider pushes on a pad that rubs on a rotating element.  FIG. 42C  is a side view of a useful embodiment of another braking assembly, where the rider presses down their foot on a foot support connected by a brake rod to a brake fin. 
         FIG. 43A  is a plan view of a useful embodiment of another thrust assembly, where left and right foot supports slide along left and right slide paths.  FIG. 43B  is a side view of a useful embodiment of another thrust assembly, where a foot holder is attached to a foot support that is connected to a thrust fin.  FIG. 43C  is a side view of the useful embodiment of the thrust assembly of  FIG. 43B , where in this figure, the foot holder is pushing the foot support forward.  FIG. 43D  is a side view of a useful embodiment of another thrust assembly, where a foot holder is attached to a rotary foot support that is connected to a thrust fin.  FIG. 43E  is a side view of the useful embodiment of the thrust assembly of  FIG. 43D .  FIG. 43F  is an end view of a useful embodiment of another thrust assembly. 
         FIG. 44  is a side view of a useful embodiment of another thrust assembly, where two four-bar linkages are used. 
         FIG. 45A  is a side view of a useful embodiment of another thrust assembly, where two four-bar linkages are used.  FIG. 45B  is a side view of a useful embodiment of another thrust assembly, similar to  FIG. 45A , but which adds a third four-bar linkage. 
         FIG. 46A  is a side view of a useful embodiment of another thrust assembly, where a four-bar linkage is used.  FIG. 46B  is a side view of a useful embodiment of another thrust assembly, where a four-bar linkage is used similar to  FIG. 46A , but with additional links added. 
         FIG. 47A  is a side view of a useful embodiment of another thrust assembly, where a four-bar linkage is used.  FIG. 47B  is a rear end view of a useful embodiment of another thrust assembly.  FIG. 47C  is a side view of a useful embodiment of a thrust fin assembly. 
         FIG. 47D  is a side view of a useful embodiment of another thrust assembly, where a four-bar linkage is used.  FIGS. 47E-47F  are side views of useful embodiments of crank assemblies for providing thrust. 
         FIG. 48A  is a side view of a useful embodiment of another thrust assembly, where a foot support may be pumped up and down to rotate a shaft.  FIG. 48B  is a plan view of the useful embodiment of  FIG. 48A . 
         FIG. 49A  is a side view of a useful embodiment of another thrust assembly, where one or more thrust fins rotate relative to foot supports.  FIG. 49B  is a side view of the useful embodiment of  FIG. 49A  during a recovery phase.  FIG. 49C  is a plan view of the useful embodiment of  FIGS. 49A and 49B , where the rider uses their foot to move the foot support. 
         FIG. 49D  is a plan view of a useful embodiment of another thrust assembly, where a thrust fin rotates relative to a foot support. 
         FIG. 50A  is a side view of a useful embodiment of a foot holder and a foot support, where the foot holder comprises protrusions that mate with sockets on the foot support.  FIG. 50B  is a side view of a useful embodiment of the foot holder and a foot support of  FIG. 50A .  FIG. 50C  is a side view of a useful embodiment of guide wheels and constrained within a guide.  FIG. 50D  is a rear end view of a useful embodiment of guide wheels of  FIG. 50C .  FIGS. 50E, 50F, and 50G  are a side views of a useful embodiment of a foot support, where a thrust fin is connected to the foot support by a connector.  FIG. 50H  is a rear end view of a useful embodiment of the foot support of  FIGS. 50E, 50F, and 50G .  FIG. 50I  is a side view of a useful embodiment of a foot support similar to  FIG. 50E , but where the thrust fin is positioned to the rear of the foot support.  FIG. 50J  is a plan view of a useful embodiment of the foot support of  FIGS. 50E, 50F, 50G, and 50H .  FIG. 50K  is a plan view of a useful embodiment of the foot support of  FIG. 50J , where wheels with vertical axes (i.e., out of the paper) support torsional force.  FIG. 50L  is a plan view of a useful embodiment of the foot support of  FIG. 50J , where wheels with vertical axes (i.e., out of the paper) support torsional force. 
         FIG. 51A  is a side view of a useful embodiment of a foot holder and a foot support guided by a linear bearing.  FIGS. 51B, 51C, and 51D  are a side views of a useful embodiment of a foot support.  FIG. 51E  is a plan view of a useful embodiment of the foot support of  FIG. 51B , where the roller wheels are guided by a linear bearing.  FIG. 51F  is a rear end view of a useful embodiment of the foot support of  FIG. 51B .  FIG. 51G  is a side view of a useful embodiment of a foot holder and a foot support guided by a linear bearing.  FIG. 51H  is a side view of the useful embodiment of  FIG. 51G  during the thrust phase.  FIGS. 51I-51J  are plan views of useful embodiments of the foot support of  FIGS. 51G and 51H .  FIG. 51K  is a plan view of a useful embodiment of the foot support of  FIG. 51J . 
         FIGS. 52A-52B and 52D  are side views of useful embodiments of foot holders and foot supports.  FIG. 52C  is a side view of a useful embodiment of the foot holder and the foot support of  FIG. 52B .  FIG. 52E  is a side view of a useful embodiment of the foot holder and the foot support of  FIG. 52D .  FIGS. 52F-520  provide useful embodiments of various thrust assemblies and components where a thrust fin automatically rotates into the water. 
         FIG. 53A  is a rear end view of a useful embodiment of another thrust assembly, where a foot holder is mated with a foot support.  FIG. 53B  is a side view of a useful embodiment of another thrust assembly, where a foot holder is mated with a foot support.  FIG. 53C  is a plan view of a useful embodiment of another thrust assembly, where a foot rests on a foot support.  FIG. 53D  is a side view of a useful embodiment of another thrust assembly, where a foot holder rests on a foot support.  FIGS. 53E-35F  are side views of useful embodiments of portions of thrust assemblies guided by linear bearings.  FIGS. 53G-53H  are rear end views of useful embodiments of other thrust assemblies, where foot holders are mated with foot supports.  FIG. 53I  is a side view of a useful embodiment of a thrust fin assembly comprising a detent.  FIG. 53J  is a side view of a useful embodiment of the thrust fin assembly of  FIG. 53I .  FIG. 53K  is a side view of a useful embodiment of a thrust fin assembly comprising a detent.  FIG. 53L  is a side view of a useful embodiment of the thrust fin assembly of  FIG. 53K .  FIG. 53M  is a plan view of a useful embodiment of another thrust assembly which may comprise any of the useful embodiments of  FIGS. 53A-53L . 
         FIG. 54A  is a perspective view of a useful embodiment of another thrust assembly, where a foot support is connected to a thrust fin.  FIG. 54B  is a perspective view of a useful embodiment of a thrust fin assembly comprising a detent.  FIG. 54C  is a perspective view of the useful embodiment of the thrust fin assembly of  FIG. 54B .  FIG. 54D  is a side view of a useful embodiment of another thrust assembly comprising spring-loaded one-way flaps. 
         FIG. 54E  is a side view of a useful embodiment of the thrust assembly of  FIG. 54D  comprising a spring-loaded one-way flap.  FIG. 54F  is a side view of the useful embodiment of the thrust assembly of  FIG. 54E  comprising a spring-loaded one-way flap.  FIG. 54G  is a side view of a useful embodiment of another thrust assembly, where a thrust paddle for an SUP is stable in either of two positions.  FIG. 54H  is a side view of the useful embodiment of the thrust assembly of  FIG. 54G .  FIG. 54I  is a side view of a useful embodiment of another thrust assembly, where a thrust paddle for an SUP is stable in either of two positions.  FIG. 54J  is a side view of the useful embodiment the constraint guide of  FIG. 54I . 
         FIG. 55A  is a rear end view of a useful embodiment of another thrust assembly, where a thrust paddle for an SUP is stable in either of two positions.  FIG. 55B  is a side view of the useful embodiment of the thrust assembly of  FIG. 55A .  FIGS. 55C-55D  are side views of useful embodiments of the constraint guide of  FIG. 55A . 
         FIG. 56A  is a combined side/perspective view of a useful embodiment of another thrust assembly, where a rider is standing with their feet on translatable foot supports, and with their hands on handlebars.  FIG. 56B  is a combined side/perspective view of a useful embodiment of another thrust assembly, where a rider is seated on a seat with a foot contacting a translatable foot support, and their hands on handlebars. 
         FIG. 57A  is a combined side/perspective view of a useful embodiment of another thrust assembly of an SUP, where a rider may stand with a foot on a translatable foot support, and place their hand on a hand lever.  FIG. 57B  is a combined side/perspective view of a useful embodiment of another thrust assembly for an SUP, where a rider may stand with a foot on a translatable foot support, and place their hand on a handle comprising a lever. 
         FIG. 58  is a perspective view of a useful embodiment of another thrust assembly for an SUP comprising translatable foot supports. 
         FIG. 59A  is a side view of a useful embodiment of another thrust assembly for an SUP comprising a translatable foot support.  FIG. 59B  is a plan view of the useful embodiment of the thrust assembly of  FIG. 59A . 
         FIG. 60  is a plan view of another useful embodiment of a thrust assembly similar to  FIG. 59B , but where there are two separate paddle handles. 
         FIG. 61A  is a plan view of another useful embodiment of a thrust assembly, where right and left foot supports are connected by joints to right and left connectors which are connected by joints to right and left paddle handles, where the paddle handles have paddle blades.  FIG. 61B  is a side view of the embodiment of a handle guide assembly.  FIG. 61C  is a plan view of another useful embodiment of a thrust assembly, where a foot support is connected by joints to right and left connectors which are connected by joints to right and left paddle handles, where the paddle handles have paddle blades.  FIG. 61D  is a plan view of another useful embodiment of a thrust assembly, where a foot support is connected by a joint to a multi-bar linkage. 
         FIG. 62A  is a side view of another useful embodiment of a thrust assembly comprising a right and left flotation device for the right and left feet of a rider.  FIG. 62B  is a side view of the useful embodiment of the thrust assembly of  FIG. 62A . 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The subject invention is further described in detail hereunder referring to the embodiments provided in the drawings. The following descriptions exemplify only some of the types of movements, mechanisms, and electronics that provide thrust, braking, and turning of a buoyant member, and other desired effects. Mechanisms provided may be substituted with electronic sensors and actuators, and gears provided may be substituted with pulleys and cables, and vice versa. In many cases, gears, pulleys, and cables are shown to provide a simple example of the functional relationship and relative movement between a plurality of members, but typically, any functionally equivalent apparatus to the provided gears, pulleys, and cables may be substituted. Additionally, throughout this application, the thrust, steering, or braking controlling and actuating assemblies provided by one embodiment may be readily combined with, used with, or substituted for, another embodiment. For example, for clarity of the drawings, a simplified embodiment might show a thrust control and actuation assembly, but not show a steering or braking control or actuation assembly; however, any steering or braking control or actuation assembly provided by another embodiment may be combined with, used with, or substituted for, such simplified embodiment as if the braking control or actuation assembly were explicitly provided in the simplified embodiment. Additionally, throughout this application, the term SUP includes, but is not limited to, a stand-up paddle board, surf board, kayak, canoe, pontoon, or any of a variety of buoyant objects, boards, boats, inflatable devices, and the like, or any other functionally similar floatation or buoyant apparatus, where the apparatus may comprise a plurality of floatation or buoyant members, and where the apparatus is capable of providing buoyancy support for at least one user or rider in a fluid, which may be water. An outline of a shoe shown on an SUP or foot support exemplifies where the rider typically puts their feet on the SUP or foot support, and there need not be an actual shoe or other special foot holder. 
       FIG. 1A  is a side view of a first useful embodiment of the subject invention. It comprises a translation assembly in a forward position and attached to a standup paddle board (SUP)  100  having a front portion  126  and a rear portion  127 . Although the profile of a generic SUP  100  is shown, as mentioned in the previous paragraph, any of a variety of buoyant objects, boards, boats, inflatable devices, and the like may be used in place of SUP  100 . In  FIGS. 1A-1D , some ripples of the water  131  are shown below and not contacting the SUP  100 ; although, in typical operation, the bottom surface of the SUP  100  is substantially in contact with the water  131  and supported by the water  131  due to the buoyancy of the SUP  100 , so the average level of the water  131  is typically somewhere between the bottom surface and top surface of the SUP  100 . 
       FIGS. 1A-1D  provide the case where the translation assembly comprises a linear guide assembly, where the linear guide assembly comprises a carriage  104  for linearly moving with low friction along the length of the rail  158 . The rail  158  is affixed to the SUP  100 , and the rider of the watercraft  159  typically places one foot on or in a foot support  105 , such as a boot, foot cradle, or sock, that is affixed to the carriage  104 . Such foot support  105  is typically affixed to the carriage  104  near the toe portion of the foot support  105  using toe fastener  106 , where the toe fastener typically comprises a hinge, Velcro, pin, axel, clip, or other fastening technique permitting the toe region of the foot support  105  to pivot relative to the carriage  104 . The foot support  105  is typically flexible near the ball of the food for permitting the heel region of the foot support  105  to move out of contact with the carriage  104 , such as up and off the carriage  104 , similar to how a Nordic ski boot flexes with a Nordic ski binding, such as a cross-country ski binding, where the skier&#39;s toe region is affixed to the ski and the skier&#39;s heel region remains relatively free to move. 
     For better balance, and to allow the rider to use and exercise both legs, and to provide a gliding sensation for the rider that is similar to the gliding sensation perceived by a cross-country skier, there are typically two carriage/rail assemblies, one for each foot, arranged parallel to each other and each affixed parallel to the SUP  100 ; however, only one carriage/rail assembly is required. 
     As shown in  FIGS. 1A-1D , the linear guide assembly comprises a linear guide rail  158  with a rear portion  101 , a forward portion  130 , and a top surface  110 . A carriage  104  is guides along rail  158  with bearings  146 . The carriage  104  for the rail  158  may comprise ball bearings, roller bearing such as cylindrical roller bearings, bushings, and the like to support up/down motion, side-side motion, or both. The bearings and bushings may comprise steel, stainless steel, aluminum, plastic, fabric, or other materials depending on the design, stability and wear requirements. 
     Companies that provide useful linear guides, linear rails, linear bearings, and the associated carriages, blocks, and the like include: Igus (www.igus.com), and in particular their DryLin® T Low-Profile Linear Guides, Drylin SWUM/EWUM supported steel shaft with Drylin OJUI-11-xxTW straight bearing open twin pillow block; Hiwin HG Series such as their HGW15 Flange Block Linear Guides; VBX and their rail guideway system with flanged square slide unit linear motion, such as part number Kit7821; Thomson bearing ball carriage, such as part number 511H25A1; and various Chinese suppliers provide SBR10 fully supported linear rail shaft rod with SBR10UU open linear slide bearing (or bushing) blocks (or carriages), such as might be used for CNC (computer numerical control) equipment. 
       FIGS. 1A  (side view) and  1 B (rear end view) show the translation assembly in a typical starting position for the “thrust phase” of the watercraft  159 ; whereas,  FIGS. 1C  (side view) and  1 D (rear end view) show the translation assembly at a typical starting position for the “recovery phase” of the watercraft  159 . In the thrust phase, the rider&#39;s foot is secured relative to the foot support  105 , and the rider pushes their foot backward in the direction of the arrow  107 . The rider may put their hands on handlebar grips  132  and  143 , and use the handlebar grips to provide leverage to push against to drive each of their feet backwards, one at a time, or together, similar to pushing a sled. Similarly, the rider may put their hands on handlebar grips  132  and  143 , and use the handlebar grips to provide leverage to pull against to drive each of their feet forward, one at a time, or together. 
     As the rider&#39;s foot presses against the foot support  105 , the carriage  104  slides in the direction of the arrow  107  toward the rear portion  101  of the rail  158 . As the carriage  104  moves backward, the engaging portion  109  of sector  108  engages with the top  110  of the rail  158 , causing it to rotate counter clockwise (CCW) in  FIG. 1A  in the direction of the arrow  111 . Any convenient means may be used to engage the engaging portion  109  of the sector  108  with the top  110  of the rail  158 . For instance, the engaging portion  109  may comprise gear teeth that engage with mating gear teeth in the top  110  of the rail  158 . Alternatively, the engaging portion  109  may include an elastic coating, such as rubber, that grips with the top  110  of the rail  158 , causing the sector  108  to rotate CCW in  FIG. 1A  when the carriage  104  moves backward. 
     Sector  108  rotates around the axis  141 , and is affixed to the carriage  104  by the positioning member  114 , which is affixed to the positioning member  142 , which is affixed to the carriage  104 . In practice, positioning members  114  and  142  may be largely different in actual structure, but are shown here as discrete members to illustrate their positioning function. 
     The worm gear  112  is affixed to the sector  108 , either explicitly, or affixed to the same rotary shaft  151  with axis  141 , such that as the sector  108  rotates CCW in  FIG. 1A , the worm gear  112  also rotates CCW with the sector  108 . The spiral teeth  148  of the worm gear  112  mesh with the straight teeth  147  of the worm wheel  113 , where their axes of rotation are perpendicular. As the worm gear  112  rotates CCW in  FIG. 1A , the worm wheel  113  rotates clockwise (CW) in  FIG. 1B , as indicated by the arrow  149  in  FIG. 1B . The gear ratio is selected to provide the desired mechanical advantage. 
     When the carriage  104  moves backward, the worm wheel  113  rotates CW in  FIG. 1B  around axis  150 , which is supported by positioning member  115  in  FIG. 1A . The positioning member  115  is rotatably connected to the positioning member  117  at the rotation joint  116 , and positioning member  115  is able to rotate relative to the positioning member  117  about the axis  150 . The positioning member  117  is affixed to the positioning member  142 , which is affixed to the carriage  104 . The positioning member  115  is affixed to the positioning member  118 , which is rotatably connected to the paddle arm  119  at the rotation joint  120  about a vertical axis in  FIG. 1A . 
     As the rider&#39;s foot moves backward, the foot support  105  causes the carriage  104  to slide backward on the rail  158 , causing the sector  108  and the worm gear  112  to rotate CCW in  FIG. 1A , causing the worm wheel  113  to rotate CW in  FIG. 1B , causing the positioning members  115  and  118  to rotate CW in  FIG. 1B , causing the paddle arm  119  to rotate CW in  FIG. 1B , and ultimate causing the paddle blade  121  that is firmly affixed to the paddle arm  119  also to rotate CW in  FIG. 1B . 
     As the paddle arm  119  rotates CW in  FIG. 1B , the rotation member  124 A that is firmly affixed to the paddle arm  119  comes into contact with the rotator member  125  that is firmly affixed to the positioning member  117 . This contact causes the paddle arm  119  and the paddle blade  121  to rotate about the rotation joint  120 , such that the paddle blade  121  rotates from the back position  123  to the side position  122 . A typical rotation amount is 90 degrees. Associated with rotation joint  120 , but not shown in any of  FIGS. 1A-1D , is a first paddle limit stop that prevents the paddle blade  121  from rotating past the side position  122  when rotating from the back position  123 . The first paddle limit stop may take the form of a protrusion from the positioning member  115  that contacts the rotation member  124 A and prevents the paddle arm  119  from continuing to rotate about the rotation joint  120 . As the rider&#39;s foot continues to move the carriage  104  backward, the paddle arm  119  and paddle blade  121  rotate CW in  FIG. 1B  and at least a portion of the paddle blade  121  enters the water  131  in a functional orientation that uses the first paddle limit stop to help apply pressure against the water  131  as the rider continues to push the carriage  104  backward. 
     As the rider&#39;s food continues to press the carriage  104  backward, the paddle blade  121  that is now at least partially extended into the water  131  continues to press against the water, providing forward thrust and moving the SUP  100  forward relative to the water  131 . Typically the farther backward the carriage  104  travels, the more the heel of the rider will rise up, whereas the rider&#39;s toes and ball of their foot typically remains pressing against the carriage  104  through foot support  105  where the foot support  105  is affixed by toe fastener  106  to carriage  104 . 
     The arc length of the sector  108  may be selected such that as the paddle blade  121  is extended to the desired position in the water  131 , the engaging portion  109  exits engagement with the mating top portion  110  of rail  158 , so the paddle blade  121  is not lowered farther into the water  130 . Another way to control the maximum distance that the paddle blade  121  is lowered into the water  130  is to alter the engagement structure of the engaging portion  109  such that it no longer engages the top portion  110  of rail  158 . Another way to control the maximum distance that the paddle blade  121  is lowered into the water  130  is to alter the worm gear  112  or worm wheel  113  so they no longer rigidly engage each other and instead slip relative to each other when the paddle blade  121  reaches its desired extension into the water  130 . A clutch or other convenient technique that is set to slip when the paddle blade  121  reaches the desired position may also be used. 
     After the rider has pushed their foot backward while propelling the SUP  100  forward, the “recovery phase” can begin, as shown in  FIGS. 1C and 1D . In  FIG. 1C , the carriage  104  is shown positioned near the rear portion  101  of the rail  158 . The carriage  104  may remain in this position indefinitely; although, the associated paddle blade  121  will no longer provide forward thrust for the SUP  100  in this position. In this position near the rear portion  101  of the rail  158 , the paddle blade  121  is at least partially extended into the water  131 . When the carriage  104  stops moving relative to the rail  158 , if the SUP  100  continues to glide forward relative to the water  131 , the water  131  can cause the paddle blade  121  and paddle arm  119  to rotate about the rotation joint  120  away from the first paddle limit stop, so while at least a portion of the paddle blade  121  is still extended into the water  131 , the paddle blade  121  won&#39;t cause drag due to the relative movement of the water  131  or the air as the SUP  100  continues to glide forward. 
     To start the recovery phase, the rider moves their foot forward causing the foot support  105  to move forward in the direction of the arrow  154  toward the front portion  130  of the rail  158 . As the foot support  105  moves forward, the carriage  104  also moves forward. 
     As the carriage  104  moves forward, the engaging portion  109  of sector  108  again engages with the top  110  of the rail  158 , and this time causing it to rotate clockwise (CW) in  FIG. 1C  in the direction of the arrow  153 . 
     The worm gear  112  is affixed to the sector  108 , either explicitly, or affixed to the same rotary shaft, such that as the sector  108  rotates CW in  FIG. 1C , the worm gear  112  also rotates CW with the sector  108 . The spiral teeth of the worm gear  112  mesh with the straight teeth of the worm wheel  113 , where their axes of rotation are perpendicular. As the worm gear  112  rotates CW in  FIG. 1C , the worm wheel  113  rotates counter clockwise (CCW) in  FIG. 1D  as indicated by the arrow  152  in  FIG. 1D . The gear ratio is selected to provide the desired mechanical advantage for raising the paddle blade  121  at the desired rate and with the desired torque. 
     As the rider&#39;s foot moves forward, the foot support  105  causes the carriage  104  to slide forward on the rail  158 , causing the sector  108  and the worm gear  112  to rotate CW in  FIG. 1C , causing the worm wheel  113  to rotate CCW in  FIG. 1D , causing the positioning members  115  and  118  to rotate CCW in  FIG. 1D , causing the paddle arm  119  to rotate CCW in  FIG. 1D , and ultimate causing the paddle blade  121  that is firmly affixed to the paddle arm  119  also to rotate CCW in  FIG. 1D . 
     As the paddle arm  119  rotates CCW in  FIG. 1D , the rotation member  124 B that is firmly affixed to the paddle arm  119  comes into contact with the rotator member  125  that is firmly affixed to the positioning member  117 . This contact causes the paddle arm  119  and the paddle blade  121  to rotate about the rotation joint  120 , such that the paddle blade  121  rotates from perpendicular to the SUP  100  to being in the line of the long direction of the SUP  100 . A typical rotation amount is 90 degrees. Associated with rotation joint  120 , but not shown in any of  FIGS. 1A-1D , is a second paddle limit stop that prevents the paddle blade  121  from rotating past the back position  123  shown in  FIG. 1A . The second paddle limit stop may take the form of a protrusion from the positioning member  115  that contacts the rotation member  124 B and prevents the paddle arm  119  from continuing to rotate about the rotation joint  120 . As the rider&#39;s foot continues to move the carriage  104  forward, the paddle arm  119  and paddle blade  121  rotate CCW in  FIG. 1D  typically until mostly vertical, or a little past vertical to rest against a resting member (not shown); although, the paddle arm  119  and paddle blade  121  may be rotate to any desired position. 
     As the rider&#39;s food continues to press the carriage  104  forward, the more the heel of the rider will lower toward the carriage  104 , and typically eventually coming into contact. 
     In  FIGS. 1A and 1C , the rail  158  is shown strapped onto the SUP  100  using straps  103 . In these figures, the rail  158  is shown to have a front-end support  129  and a rear-end support  102  that are secured to the SUP  100  using front strap  128  and rear strap  103 . The straps  128  and  103  may extend all the way around the bottom of the SUP  100  to each form a complete loop around the SUP  100 , or the straps may be anchored to an anchor on the surface of the SUP  100 . Such an anchor is typically on the top surface of the SUP  100 . Front-end support  129  and rear-end support  102  may also be fastened to the SUP  100  by other effective means, including but not limited to screwing them to the top surface of the SUP  100 , or by fastening each to a bracket that is attached to the SUP  100 . Such a bracket may be attached to the SUP  100  by any effective means, typically to the top surface, and typically using screws, glue, Velcro, tape, and the like. Front-end support  129  and rear-end support  102  may also be glued, Velcroed, or taped to the SUP  100 . 
     Steering of the watercraft  159  may be controlled by the rider in one of a variety of ways. A first way to steer the watercraft  159  is using a handlebar. The handlebar comprises a right handlebar portion  144  with right handlebar grip  132 , and a left handlebar portion  145  with left handlebar grip  143 . The right and left handlebar portions,  144  and  145 , are connected to the handlebar neck  134 . The handlebar neck  134  is connected by rotary hinge  136  to handlebar support  135 , which is then connected to the SUP  100 , and typically connected to the front portion  126  of the SUP  100 . In  FIGS. 1B and 1D , for convenience of the drawing, the handlebar neck  134  is not necessarily shown centered equidistant from the right and left edges of the SUP  100 ; however, in practice, the handlebar neck  134  is typically centered equidistant from the left and right edges of the SUP  100 . The rotary hinge  136  may be any means to allow the handlebar neck  134  to rotate relative to the SUP  100 . The rotary hinge  136  may simply be comprised of a hole in the SUP that the handlebar neck  134  fits into that allows rotation. The handlebar support  135  may comprise a bracket that is attached to the SUP  100 , where such a bracket is typically attached to the top surface of the SUP  100 . 
     When handlebars are used to steer the watercraft  159 , turning the handlebar neck  134  may control one or more rudders, such as the rudder  137 . The rudder  137  is connected to the rudder base  157  by rudder connector  156 . Typically, the rudder connector  156  is a rotary hinge, but it may comprise any means that allows the rudder  137  to move relative to the rudder base  157 . The rudder base  157  is typically attached to the bottom side (that is, the water side) of the rear portion  127  of the SUP  100 . A typical attachment may include inserting the rudder base  157  into a slot in the SUP  100  intended for non-rotating rudders. The rudder base  157  may also be affixed directly to the bottom side of the rear portion  127  of the SUP  100 , such as by screwing, snapping, clipping, or any other convenient connection means. 
     Although not shown in  FIGS. 1A-1D  for clarity, the handlebar neck  134  may mechanically or electrically control the position of the rudder  137 . When the handlebar neck  134  is mechanically connected to the rudder  137 , the connection may comprise one or more rigid links, or may comprise one or more flexible links. A useful flexible link comprises a Bowden cable, similar to a bicycle brake cable, where a flexible cable is positioned inside a flexible outer sheath. Another useful flexible link comprise a flexible cable routed from the handlebar neck  134  to the rudder  137 , where the flexible cable routed such that it is always in tension, similar to a bicycle shift cable. Such routing of the flexible cable may route the cable in a straight line, or around one or more cams, rollers, pins, sliders, and the like that redirect the cable to a new direction while maintaining the cable tension. Another useful flexible link comprises two opposing flexible cables. When two opposing flexible cables are used without the flexible sheath of a Bowden cable, typically a first flexible cable from a first portion of the handlebar neck  134  pulls the rudder  137  in a first direction, and a second flexible cable from a second portion of the handlebar neck  134  pulls the rudder  137  in a second direction that is opposite to the first direction. Another useful flexible link comprises a single flexible cable that is typically used in opposition with a return spring. When the single flexible cable is pulled due to the turning of the handlebar neck  134  to turn the rudder  137 , the return spring provides tension that opposes the pulling. When the handlebar neck  134  is returned to its original unturned position such that the single flexible cable is no longer pulled, the return spring continues to apply a tension until the single flexible cable returns to the position it was in before it was initially pulled by the turning of the handlebar neck  134 . 
     Although not shown in  FIGS. 1A-1D , the handlebar neck  134  may electrically control the position of the rudder  137 . When the handlebar neck  134  electrically controls the position of the rudder  137 , typically the position of the handlebar neck  134  is sensed by a rotary position sensor, such as a rotary encoder, an optical encoder, a magnetic rotary encoder, a potentiometer, and the like. The rotary position that is sensed is then transmitted as a position signal, either using wires or transmitted wirelessly, to a rudder actuator that receives the position signal and actuates the rudder  137  to a position corresponding to the position signal. Such a rudder actuator may include an electric rotary motor or an electric linear actuator. 
     A second way to steer the watercraft  159  is using a plurality of paddle blades, such as paddle blade  121 . When a paddle blade, such as paddle blade  121  is positioned on both the left and right sides of the rider when standing on the SUP  100 , where a right paddle blade is controlled by the rider&#39;s right foot, and a left paddle blade is controlled by the riders left foot, if the rider slides their right foot forward and backward more than they slide their left foot forward and backward, they will impart more forward thrust to the right side of the SUP  100 , causing the SUP  100  to turn left. Similarly, if the rider slides their left foot forward and backward more than they slide their right foot forward and backward, they will impart more forward thrust to the left side of the SUP  100 , causing the SUP  100  to turn right. This turning technique employing relative velocity of two sides is similar to how a bulldozer turns. 
     A third way to steer the watercraft  159  is using selective braking of right and left braking fins. The right handlebar grip  132  has an associated right handbrake lever  133 , and left handlebar grip  143  has an associated left handbrake lever  160 . The right handbrake lever  133  controls the position of the right brake fin  138 . When right handbrake lever  133  is pulled toward the right handlebar grip  132 , the right brake fin  138  extends down, rotating about an axis  155  through an arc  140 , to a braking position  139 . The right handbrake lever  133  may communicate position information with the right brake fin  138  using any convenient method, including but not limited to a flexible linkage, such as a Bowden cable, a flexible cable supported by cable supports, a plurality of rigid articulated links, a wireless signal, such as an electromagnetic or optical signal, and the like. 
     Similarly, the left handbrake lever  160  controls the position of a left brake fin (not shown). When left handbrake lever  160  is pulled toward the left handlebar grip  143 , the left brake fin extends down, rotating about an axis typically coincident with the axis  155 , through an arc, to a braking position. The left handbrake lever  160  may communicate position information with the left brake fin using any convenient method, including but not limited to a flexible linkage, such as a Bowden cable, a flexible cable supported by cable supports, a plurality of rigid articulated links, a wireless signal, such as an electromagnetic or optical signal, and the like. 
     A brake fin, such as the brake fin  138 , is positioned on both the left and right sides of the rider when standing on the SUP  100 , where the right brake fin  138  is controlled by the right handbrake lever  133 , and a left brake fin is controlled by the left handbrake lever  160 . When the rider engages the right handbrake lever  133  and moves it toward the right handlebar grip  132 , the right brake fin  138  extends down, rotating about the axis  155  through the arc  140 , to the braking position  139 , which applies a drag force to the right side of the SUP  100 , causing the SUP  100  to turn right. Similarly, when the rider engages the left handbrake lever  160  and moves it toward the left handlebar grip  143 , the left brake fin (not shown) extends down, rotating about an axis typically coincident with the axis  155 , through an arc to the braking position which applies a drag force to the left side of the SUP  100 , causing the SUP  100  to turn left. This turning technique employing relative velocity of two sides is similar to how a bulldozer turns. 
     Another description of  FIGS. 1A-1D  follows: 
     Recovery Phase ( FIGS. 1C and 1D ): The partial sector  108  (of a disk) has a compressible frictional surface  109  that will grip the linear rail  158 . When the boot  105  slides the platform  104  forward  154  (i.e., the Recovery Phase), the partial sector  108  of a disk rotates clockwise  153  (CW) in the side view (of  FIG. 1C ), causing the worm gear  112  to rotate, causing the worm wheel  113  to rotate and raise the paddle arm  119  and paddle blade  121 . The paddle blade  121  may have already rotated from side  121  to back position  123  due to water pressure, but if not, during raising, the rotation pin  124 B on the paddle arm  119  hits the rotator pin  125  on the platform  104 , causing the paddle arm  119  to rotate the paddle blade  121  back  123  (in line with the SUP) to reduce wind resistance. Since the partial sector  108  is not a complete disk, when the trailing edge of the sector  108  leaves contact with the linear rail  158 , the paddle arm  119  no longer moves, and the trailing edge of the partial sector  108  drags along the top  110  of the linear rail  158 . 
     Thrust Phase ( FIGS. 1A and 1B ): The operation is largely the opposite of the Recovery Phase. At any point while the boot  105  is moving forward, if it begins to slide backward  107 , the dragging trailing edge of the partial sector  108  grips the linear rail  158  and begins to rotate counter clockwise  111  (CCW) in the side view (of  FIG. 1A ). The rubber, or any convenient compressible, frictional material, will compress and grip the linear rail  158  enough that the partial sector  108  will rotate from the leading edge (which had been the dragging trailing edge during the Recovery Phase) to the trailing edge. During rotation CCW  111 , the worm gear  112  rotates, rotating the worm wheel  113  CW  149  in the end view (of  FIG. 1B ), and thus lowering the paddle arm  119 , and lowering the paddle blade  121  into the water  131 . While the paddle arm  119  is lowering, the rotation pin  124 A hits the rotator pin  125  which rotates the paddle blade  121  from rotated back to rotated side  122  for entry. The rotation may actually rotate the blade to a point slightly forward to the direction of SUP (standup paddle board)  100  travel, to account for the relative speed of the SUP  100  to the water  131 . Once the boot  105  has moved backward  107  a little, the paddle blade  122  will be in the water and thrusting backward. Additional apparatus (not shown) may change the angle of the paddle blade  122  during thrust motion to optimize thrust. After the paddle blade  122  has entered the water  131  to the desired depth, the partial sector  108  will have rotated from its leading edge to its trailing edge, and will then drag its trailing edge along the linear rail  158  until the boot  105  moves forward  154 , causing a transition back to the Recovery Phase operation. When the boot  105  stops moving backward  107 , water pressure against the paddle blade will cause the blade  121  to rotate CW in the side view (of  FIG. 1C ). Typically, the paddle blade will rotate no more than 90 degrees to point straight back  123  (in  FIG. 1C ), before hitting a rotational limit stop. If the SUP  100  motion ceases, the paddle blade will then rotate back down  121  (in  FIG. 1C ) into the water  131  due to gravity. Either way, when the boot  105  slides forward  154  during the beginning of the Recovery Phase ( FIG. 1C ), the rotation pin  124 B on the paddle arm  119  will rotate the blade to point backwards  123  (in  FIG. 1C ) when the rotation pin  124 B comes into contact with the rotator pin  125 . 
       FIGS. 2A-2C  provide alternative embodiments of the sector  108  that rotates the worm gear  112  in  FIGS. 1A-1D .  FIG. 2A  provides an embodiment similar to that shown in  FIGS. 1A-1D , where a sector  108  is capable of rotating about the axis  141  as the axis  141  translates parallel to the rail  110 . The axis  141  is supported by a carriage (not shown in  FIG. 2A ) that is supported by the rail  110 , where the carriage is capable of translating relative to the rail  110 . The sector  108  comprises an engaging portion  109  for engaging with the top portion  110  of the rail  158 . Any convenient means may be used to engage the engaging portion  109  of the sector  108  with the top  110  of the rail  158 . For instance, the engaging portion  109  may include an elastic region, such as rubber, that grips with the top  110  of the rail  158  as the axis  141  translates parallel to the rail  110 . 
       FIG. 2B  provides a second embodiment for the sector, where a sector  200  is capable of rotating about the axis  141  as the axis  141  translates parallel to the rail  110 . The axis  141  is supported by a carriage (not shown in  FIG. 2B ) that is supported by the rail  110 , where the carriage is capable of translating relative to the rail  110 . The sector  200  comprises an engaging portion  201  for engaging with the top portion  110  of the rail  158 . Any convenient means may be used to engage the engaging portion  201  of the sector  200  with the top  110  of the rail  158 . For instance, the engaging portion  201  may include an elastic region, such as rubber, that grips with the top  110  of the rail  158  as the axis  141  translates parallel to the rail  110 . 
     As shown in  FIG. 2B , sector  200  comprises rotary members on each end, such as wheels, cylinders, and the like, that rotate when in contact with the rail  110  or a shoulder of the rail  110 . A first rotary member  202  rotates relative to the sector  200  about axis  203 , which may comprise a bearing, bushing, and the like to reduce rotary friction. The first rotary member  202  rotates freely about the axis  203  in a clockwise (CW) sense in  FIG. 2B , but rotation is prevented, i.e., it “locks,” in the counterclockwise (CCW) sense in  FIG. 2B . A second rotary member  205  rotates relative to the sector  200  about axis  206 , which may comprise a bearing, bushing, and the like to reduce rotary friction. The second rotary member  205  rotates freely about the axis  206  in a CCW direction in  FIG. 2B , but rotation is prevented, i.e., it “locks,” in the CW direction in  FIG. 2B . 
     When the carriage translates to the left in  FIG. 2B , axis  141  also translates to the left, and the second rotary member  201  freely rotates about the axis  206 , and so the sector  200  does not rotate about the axis  141  in  FIG. 2B . 
     When the carriage translates to the right in  FIG. 2B , axis  141  also translates to the right. When the axis  141  translates to the right, the second rotary member  205  locks and is unable to rotate about the axis  206 , so the entire sector  200  rotates CW about the axis  141  in  FIG. 2B . As the carriage continues to translate to the right, the engaging portion  201  engages with the rail  110 , and causes the sector to continue to rotate CW about the axis  141  until the first rotary member  202  contacts the rail  110  or a shoulder of the rail  110 . 
     As the carriage continues to translate to the right after the first rotary member  202  contacts the rail  110 , the engaging portion  201  rotates CW until it is no longer in engaged with the rail  110 , and only the first rotary member  202  remains in contact with the rail  110  or the shoulder of the rail  110 . As the carriage continues to translate to the right from this point, the first rotary member  202  rotates freely with minimal friction in a CW sense about the axis  203 , and the sector  200  no longer rotates CW about the axis  141 . 
     When the carriage changes direction and translates to the left in  FIG. 2B , the first rotary member  202  will lock, causing the sector  200  to rotate CCW until the engaging portion  201  engages with the rail  110 , causing the sector  200  to continue to rotate CCW after the first rotary member  202  rotates out of engagement with the rail  110  or the shoulder of the rail  110 , until the second rotary member  205  contacts the rail  110  or the shoulder of the rail  110 , and rotates freely with minimal friction in a CCW sense. 
     Accordingly, the sector  200  only rotates the worm gear  112  back and forth through a limited angle, equal to the angle  208  circumscribed by the sector  200 , even as the carriage continues to translate further to the left or to the right. 
       FIG. 2C  provides a third embodiment for the sector, where sector  200  is capable of rotating about the axis  141  as the axis  141  translates parallel to the rail  110 . The axis  141  is supported by a carriage (not shown in  FIG. 2C ) that is supported by the rail  110 , where the carriage is capable of translating relative to the rail  110 . The sector  200  comprises an engaging portion  204  for engaging with the top portion  207  of the SUP  100 . In this embodiment, the engaging portion  204  may include a region with pinion teeth on the sector  200  that engages with the top rack  207  on the SUP  100  as the axis  141  translates parallel to the SUP  100 . 
     Engagement comprising a rack and pinion is representative of a family of engaging surfaces. Such engaging surfaces may comprise any convenient engaging surfaces that allow little or no slip between them. Exemplary surfaces may also comprise interlaced protrusions, such as the illustrated rack and pinion, but may also comprise surfaces that engage using friction, such as provided by rubber, plastic, knurled surfaces, rough surfaces, sand paper, and the like. 
     As shown in  FIG. 2C , and similar to  FIG. 2B , the sector  200  comprises rotary members on each end, such as wheels, cylinders, and the like, that rotate when in contact with a shoulder of the rack  207 . A first rotary member  202  rotates relative to the sector  200  about axis  203 , which may comprise a bearing, bushing, and the like to reduce rotary friction. The first rotary member  202  rotates freely about the axis  203  in a clockwise (CW) sense in  FIG. 2C , but rotation is prevented, i.e., it “locks,” in the counterclockwise (CCW) sense in  FIG. 2C . A second rotary member  205  rotates relative to the sector  200  about axis  206 , which may comprise a bearing, bushing, and the like to reduce rotary friction. The second rotary member  205  rotates freely about the axis  206  in a CCW direction in  FIG. 2C , but rotation is prevented, i.e., it “locks,” in the CW direction in  FIG. 2C . 
     When the carriage translates to the left in  FIG. 2C , axis  141  also translates to the left, and the second rotary member  201  freely rotates about the axis  206 , and so the sector  200  does not rotate about the axis  141  in  FIG. 2C . 
     When the carriage translates to the right in  FIG. 2C , axis  141  also translates to the right. When the axis  141  translates to the right, the second rotary member  205  locks and is unable to rotate about the axis  206 , so the entire sector  200  rotates CW about the axis  141  in  FIG. 2C . As the carriage continues to translate to the right, the engaging portion  204  engages with the rack  207 , and causes the sector to continue to rotate CW about the axis  141  until the first rotary member  202  contacts the shoulder of the rack  207 . 
     As the carriage continues to translate to the right after the first rotary member  202  contacts the shoulder of the rack  207 , the engaging portion  204  rotates CW until it is no longer in engaged with the shoulder of the rack  207 , and only the first rotary member  202  remains in contact with the shoulder of the rack  207 . As the carriage continues to translate to the right from this point, the first rotary member  202  rotates freely with minimal friction in a CW sense about the axis  203 , and the sector  200  no longer rotates CW about the axis  141 . 
     When the carriage changes direction and translates to the left in  FIG. 2C , the first rotary member  202  will lock, causing the sector  200  to rotate CCW until the engaging portion  204  engages with the rack  207 , causing the sector  200  to continue to rotate CCW after the first rotary member  202  rotates out of engagement with the shoulder of the rack  207 , until the second rotary member  205  contacts the shoulder of the rack  207 , and rotates freely with minimal friction in a CCW sense. 
     Accordingly, the sector  200  only rotates the worm gear  112  back and forth through a limited angle, equal to the angle  208  circumscribed by the sector  200 , even as the carriage continues to translate further to the left or to the right. 
       FIGS. 3A-3C  provide rear-end cross-sections of carriage-paddle assemblies.  FIG. 3A  is similar to the carriage-paddle assembly provided by  FIGS. 1A-1D , but where the worm wheel  113  in  FIG. 3A  is positioned below the worm gear  112 . 
       FIG. 3B  is similar to  FIG. 3A , but the partial sector shown in  FIG. 3A , which comprises the partial sector of  FIG. 2A or 2B , is replaced by the partial sector  200  of  FIG. 2C . The rack  207  of  FIG. 2C  is shown to the left of the carriage  104 , and supported by the positioning member  142 , and rotates with the worm gear  112  around axis  141 , which is connected to co-axial axis  151 , about which the worm gear  112  rotates.  FIG. 3B  also provides an alternative profile for the paddle blade  121 . 
     Although some figures only provide a single carriage-paddle assembly for the right foot of a rider, all physical implementations, whether shown so in the drawings or not, typically also comprise a mirror-imaged carriage-paddle assembly for the left foot of the rider. 
       FIG. 3C  provides a rear-end cross-section of an SUP showing both the right  300  and left  303  carriages for right and left feet of the rider. The paddle blades of  FIG. 3C  are also provided extending from each carriage, through an opening in the SUP  100 , rather than to the side of the SUP  100 . 
     The right carriage  300  is guided by the right guide  301 . As shown, a portion of the right carriage  300  is recessed in the SUP  100  below the top surface  316  of the SUP  100 . The right foot support  302  is attached to the right carriage  300 , typically removably attached near the front portion of the right foot support  302 . In this illustrative embodiment, two right paddle blades  306  and  307  extend into the water below the right carriage  300 , and their orientation is determined by the force of the water as the right carriage  300  moves forward  340  and backward  336 . 
       FIGS. 3D-3G  are plan views of the right carriage  300  of  FIG. 3C  in different positions along a linear guide  301 , and  FIG. 3H  is a side view of the right carriage  300  in the position shown in  FIG. 3G . The linear guide  301  has a bearing portion  330  and a base portion  331  with a right edge  332  and a left edge  333 . Bearings allow the right carriage  300  with base portion  328  and bearing portion  329  to move along the linear guide  301  bearing portion  330 . The right carriage  300  and left carriage  303  each have similar bearings, shown in  FIG. 3C  as ball bearings, and labeled as elements  327  in the left carriage  303 . 
     The paddle blade  306  rotates relative to the right carriage  300  about the vertical axis  325 , and the paddle blade  307  rotates relative to the right carriage  300  about the vertical axis  323 . The paddle blade  306  has a rotation limit stop  326 , and the paddle blade  307  has a rotation limit stop  324 . In  FIGS. 3C, 3E, and 3F , the paddle blades  306  and  307  are shown to be rotated about their vertical axes and resting against their respective limit stops. The right carriage  300 , paddle blades  306  and  307 , and the linear guide  301 , are positioned in an opening  341  in the SUP  100 , where the opening  341  has a right opening edge  334  in the SUP portion  318 , and the opening  341  has aleft opening edge  335  in the SUP center portion  314 . 
       FIG. 3D  shows the right carriage  300  in a forward position relative to the opening  341  in the SUP  100 , where the paddle blades  306  and  307  have been rotated by the water away from their limit stops  326  and  324 , respectively.  FIG. 3E  shows the right carriage  300  slid rearward  336  by the rider&#39;s foot. When the right carriage  300  is slid rearward  336 , movement of the paddle blade  306  relative to the water causes the paddle blade  306  to rotate counterclockwise until it reaches the limit stop  326 . Likewise, the paddle blade  307  rotates clockwise until it reaches the limit stop  324 . When the paddle blades  306  and  307  reach their limit stops, they are able to apply forward thrust against the water as the rider&#39;s foot continues to slide the carriage  300  rearward  336 .  FIG. 3F  shows the right carriage  300  moved to a farther rearward position relative to the opening  341  in the SUP  100 . 
       FIG. 3G  shows the right carriage  300  slid forward  340  by the rider&#39;s foot. When the right carriage  300  is slid forward  340 , movement of the paddle blade  306  relative to the water causes the paddle blade  306  to rotate clockwise away from the limit stop  326 . Likewise, the paddle blade  307  rotates counterclockwise away from the limit stop  324 . When the paddle blades  306  and  307  move away from their limit stops as shown, they minimize their resistance against the water as the rider&#39;s foot continues to slide the carriage  300  forward  340 . 
       FIG. 3H  is a side view of  FIG. 3G  which shows the right carriage  300  being slid forward  340  by the rider. The right foot support  302  is shown removably attached  339  to the right carriage  300 , typically removably attached near the front portion of the right foot support  302 . The opening  341  in the SUP  100  is bounded in the front of the SUP  100  by a front SUP portion  337 , and is bounded in the rear of the SUP  100  by a rear SUP portion  338 . 
     Similarly to the right carriage  300 , the left carriage  303  is guided by the left guide  304 . As shown, a portion of the left carriage  303  is recessed in the SUP  100  below the top surface  316  of the SUP  100 . The left foot support  305  is attached to the left carriage  303 , typically removably attached near the front portion of the left foot support  305 . In this illustrative embodiment, two left paddle blades  310  and  311  extend into the water below the left carriage  303 , and their orientation is determined by the force of the water as the left carriage  303  moves forward and backward. 
     The paddle blade  310  rotates relative to the left carriage  303  about the vertical axis  317 , and the paddle blade  311  rotates relative to the left carriage  303  about the vertical axis  321 . The paddle blade  310  has a rotation limit stop  320 , and the paddle blade  311  has a rotation limit stop  322 . The left carriage  303 , paddle blades  310  and  311 , and the linear guide  304 , are positioned in an opening in the SUP  100 , where the opening has a right opening edge in the SUP center portion  314 , and the opening has aleft opening edge in the SUP portion  319 . 
     In place of mechanical structure that relies on movement of a carriage to alter the position mechanically of paddle blades, an electrical system may be used. An electrical system may sense the position of the rider&#39;s foot or an associated carriage and may send a signal, which may be an electrical control signal, to an output actuator, such as a paddle blade actuator, where the signal may indicate the desired position and orientation of the paddle blade. Sensing of the position of the rider&#39;s foot or an associated carriage may employ an electrical or mechanical sensor, including but not limited to an optical encoder, a linear encoder, a rotary encoder, a potentiometer, one or more cables, an LVDT, electromagnetics, a Hall Effect sensor, a laser, and an interferometer, and the like. An output actuator, such as a paddle blade actuator, may include a rotary motor, a linear motor, an electric motor, a solenoid, and the like. The paddle blade actuator may be a radio-controlled (RC) electric motor. The signal may be sent from the carriage position sensor to the paddle blade actuator using wires, or may be sent wirelessly. When sent wirelessly, the signal may be sent using electromagnetic waves, Bluetooth, RF, light, sound, and the like. 
       FIGS. 4A-4D  provide steering and braking assemblies.  FIG. 4A  is a perspective view of an embodiment illustrating useful steering and braking assemblies associated with the SUP  100  of  FIGS. 1A-1D .  FIG. 4A  provides a handlebar for steering that comprises the right handlebar portion  144  with right handlebar grip  132 , and the left handlebar portion  145  with left handlebar grip  143 . The right and left handlebar portions,  144  and  145 , are connected to the handlebar neck  134 . The handlebar neck  134  is connected by the rotary hinge  136  to the handlebar support  135 , which is then connected to the SUP  100 , and typically connected to the front portion of the SUP  100 . 
     In  FIG. 4A , when the handlebar neck  134  is turned to the right relative to the handlebar support  135 , the lever  407  pulls on the cable tendon  408  in the sheath  409 , where the cable  408  and sheath  409  comprise a Bowden cable. When the handlebar neck  134  is turned to the left relative to the handlebar support  135 , the lever  407  pushes on the cable tendon  408  in the sheath  409 . One end of the sheath  409  is attached to the bracket  411 , and the other end of the sheath  409  is attached to the bracket  410 , where both brackets  411  and  410  are attached to the SUP  100 . One end of the cable tendon  408  is attached to the handlebar neck lever  407 , and the other end of the cable tendon  408  is attached at the location  443  on the rudder lever  444 , that is attached to the rudder rotary joint  403 . Pulling and pushing the cable tendon  408  causes the rudder  400  to turn to the desired angle. The cable tendon  408  of  FIG. 4A  may control a cable tendon such as the cable tendon  434  in  FIG. 4C  which is inside the sheath  418  attached to the rudder bracket  433 , so that when the cable tendon  408  is pulled due to turning the handlebars to the right, the cable tendon  434  that is attached to the cam  436  at the point  437  also pulls on the cam  436  that is attached to the rudder  423 , causing the cam  436  and rudder  423  in  FIG. 4C  to rotate CCW about the rotary joint  426 , causing the SUP  100  to turn to the right. When the cable tendon  408  is pushed due to turning the handlebars to the left, the cable tendon  434  that is attached to the cam  436  at the point  437  also pushes on the cam  436  that is attached to the rudder  423 , causing the cam  436  and rudder  423  in  FIG. 4C  to rotate CW about the rotary joint  426 , causing the SUP  100  to turn to the left. In the description above, the rudder  423  in  FIG. 4C  corresponds to the rudder  400  in  FIG. 4A , the rotary joint  426  in  FIG. 4C  corresponds to the rudder rotary joint  403  in  FIG. 4A , and the rudder bracket  433  in  FIG. 4C  corresponds to the rudder bracket  406  in  FIG. 4A . The rudder bracket is attached to the SUP  100 , typically being attached to the rear of the SUP and equidistant from the right and left edges of the SUP  100 . It may be attached to the location that typically is manufactured to receive a fin on an SUP. 
     In  FIG. 4A , the brake lever  412  is attached to the Bowden cable  413  that controls the position of the right brake fin  401  and left brake fin  402 . The brake lever  412  can be rotated relative to the handlebar bracket  445  about the revolute joint  446 . The brake fin  401  is capable of rotating about the rotary joint  404  relative to the rudder bracket  406 . The brake fin  402  is capable of rotating about the rotary joint  405  relative to the rudder bracket  406 . One end of the cable tendon  440  is attached to the brake lever  412 , and the other end is attached to the location  441  on the brake fin lever  442  that is attached to the brake rotary joint  404 . When the brake lever  412  is pulled, the cable tendon  440  causes at least one of the brake fins  401  and  402  to rotate, creating water drag to oppose the forward motion of the SUP  100 . 
       FIG. 4B  is a perspective view of another embodiment illustrating useful steering and a braking assemblies associated with SUP  100 ;  FIG. 4C  is a top view of the embodiment of  FIG. 4B ; and  FIG. 4D  is a side view of the right brake fin of the embodiment of  FIG. 4C .  FIGS. 4B and 4C  provide a handlebar for balance and pressing against when generating thrust. The handlebar comprises a right handlebar portion  144  with right handlebar grip  132 , and a left handlebar portion  145  with left handlebar grip  143 . The right and left handlebar portions,  144  and  145 , are connected to the handlebar neck  134 . The handlebar neck  134  is connected to handlebar support  135 , which is then connected to the SUP  100 , and typically connected to the front portion of the SUP  100 . 
     The right rudder lever  414  and right brake lever  416  each rotate about revolute joints  447  and  448 , respectively, relative to the right handlebar bracket  449 . The sheaths of the Bowden cables  418  and  420  are supported by the right handlebar bracket  449 , and have cable tendons  434  and  428 , respectively, inside the sheaths, that are attached to the right rudder lever  414  and right brake lever  416 , respectively. When the right rudder lever  414  and the right brake lever  416  are pulled, the cable tendons  434  and  428 , respectively, are translated relative to the sheaths of the Bowden cables  418  and  420 , respectively. 
     Similarly, the left rudder lever  415  and left brake lever  417  each rotate about revolute joints  450  and  451 , respectively, relative to the left handlebar bracket  452 . The sheaths of the Bowden cables  419  and  421  are supported by the left handlebar bracket  452 , and have cable tendons  435  and  429 , respectively, inside the sheaths, that are attached to the left rudder lever  415  and right brake lever  417 , respectively. When the left rudder lever  415  and the left brake lever  417  are pulled, the cable tendons  435  and  429 , respectively, are translated relative to the sheaths of the Bowden cables  419  and  421 , respectively. 
     In  FIGS. 4B-4C , the right rudder lever  414  is attached to the Bowden cable  418  that controls the position of the rudder  423 . The rudder  423  is capable of rotating about the rotary joint  426  relative to the rudder bracket  433 . The sheath of the Bowden cable  418  is attached to the rudder bracket  433  and has the cable tendon  434  inside the sheath. When the right rudder lever  414  is pulled, the cable tendon  434  that is attached to the cam  436  at the point  437  also pulls on the cam  436  that is attached to the rudder  423 , causing the cam  436  and the rudder  423  in  FIG. 4C  to rotate CCW about the rotary joint  426 , causing the SUP  100  to turn to the right. 
     The sheath of the Bowden cable  419  is attached to the rudder bracket  433  and has the cable tendon  435  inside the sheath. When the left rudder lever  415  is pulled, the cable tendon  435  that is attached to the cam  436  at the point  438  also pulls on the cam  436  that is attached to the rudder  423 , causing the cam  436  and the rudder  423  in  FIG. 4C  to rotate CW about the rotary joint  426 , causing the SUP  100  to turn to the left. 
     In  FIGS. 4B-4D , the right brake lever  416  is attached to the Bowden cable  420  that controls the position of the right brake fin  432 . The sheath of the Bowden cable  420  is attached to the rudder bracket  433 , and the cable tendon  428  is attached to the right brake fin  432  at location  430  on the lever  422 . The right brake fin  432  is capable of rotating about the rotary joint  427 A relative to the rudder bracket  433 . When the right brake lever  416  is pulled, the Bowden cable  420  causes the right brake fin  432  to rotate down creating water drag on the right side of the SUP  100  to oppose the forward motion of the SUP  100 . If only the right brake lever  416  is pulled, the unbalanced drag on the right side of the SUP  100  will also cause the SUP  100  to turn to the right. 
     In  FIGS. 4B and 4C , the left brake lever  417  is attached to the Bowden cable  421  that controls the position of the left brake fin  424 . The sheath of the Bowden cable  421  is attached to the rudder bracket  433 , and the cable tendon  429  is attached to the left brake fin  424  at location  431  on the lever  439 . The left brake fin  424  is capable of rotating about the rotary joint  427 B relative to the rudder bracket  433 . When the left brake lever  417  is pulled, the Bowden cable  421  causes the left brake fin  424  to rotate down creating water drag on the left side of the SUP  100  to oppose the forward motion of the SUP  100 . If only the left brake lever  417  is pulled, the unbalanced drag on the left side of the SUP  100  will also cause the SUP  100  to turn to the left. 
     Together with, or in place of, any mechanical structure described in this specification that provides movement of a cable or linkage to alter the position mechanically of a turnable rudder or a braking fin, an electrical system may be used. An electrical system may sense the position of an input controller, such as a handlebar, handlebar grip, lever, pedal, carriage, and the like, and may send a signal, which may be an electrical control signal, to an output actuator, such as a rudder, breaking fin, or paddle actuator, where the signal may indicate the desired position and orientation of the rudder, breaking fin, or paddle actuator. Sensing of the position of an input controller may employ an electrical or mechanical sensor, including but not limited to an optical encoder, a linear encoder, a rotary encoder, a potentiometer, one or more cables, an LVDT, electromagnetics, a Hall Effect sensor, a laser, and an interferometer, and the like. A rudder, braking fin, or paddle actuator may include a rotary motor, a linear motor, an electric motor, a solenoid, and the like. The rudder, braking fin, or paddle actuator may be a radio-controlled (RC) electric motor. The signal may be sent from the input controller sensor to the rudder, braking fin, or paddle actuator using wires, or may be sent wirelessly. When sent wirelessly, the signal may be sent using electromagnetic waves, Bluetooth, RF, light, sound, and the like. 
       FIG. 5A  is a perspective view of a useful embodiment of the invention. The SUP  500  is shown on water  501 . The handlebar  502  has right and left levers  503 A and  503 B, respectively, that may control turning, braking, and the like. The handlebar  502  may not swivel, or it may swivel around rotary joint  504  relative to the handlebar base  505  that is attached to the SUP  500  or to a mounting structure  567 . The mounting structure  567  provides a rigid structure to which other elements may be attached to position such elements relative to each other and relative to the SUP  500 . 
     The mounting structure  567  may be permanently or removably attached to the SUP  500 . When the mounting structure  567  is removably attached to the SUP  500 , it allows a standard SUP  500  to be retrofit to comprise elements of the subject invention. The mounting structure  567  may fasten to a cavity  511  in the SUP  500 . Such a cavity  511  may also be used for hand carrying the SUP  500 .  FIG. 5D  shows details of one embodiment of a protruding member that extends into to the cavity  511  for positioning and fastening. In particular, as shown in  FIGS. 5A and 5D , the protruding member may comprise a control  512  that the rider may activate to secure the mounting structure  567  to the SUP  500 . The rider may turn a portion of the control  512  to activate it. 
     In  FIG. 5A , the mounting structure  567  is also shown strapped to the SUP  500 . Any convenient strap and strap termination method may be used. In  FIG. 5A , a front strap  506  is fastened to the front-left portion of the mounting structure  567  by the strap end  507 . The front strap  506  is then fastened to the front-right portion of the mounting structure  567  with a termination  568 . The termination  568  may comprise any convenient termination and tightening means, including but not limited to a buckle, a loop, Velcro, and the like. Similarly, a rear strap  508  is fastened to the rear-left portion of the mounting structure  567  by the strap end  509 . The rear strap  508  is then fastened to the rear-right portion of the mounting structure  567  with a termination  569 . The termination  569  may comprise any convenient termination and tightening means, including but not limited to a buckle, a loop, Velcro, and the like. 
     In  FIG. 5A , the mounting structure  567  has guides on the right and left portions. The guides may comprise linear guides or comprise linear bearings. The right guide  536  is fastened to the mounting structure  567  with a front fastener  537  and a rear fastener  538 . The right guide  536  comprises a right bearing  539 . The right bearing  539  is attached to a right carriage  531  on which the rider&#39;s right foot may be placed. The right bearing  539  may comprise a rotary member, a wheel, roller bearing, ball bearing, a bushing, and the like, which allows the right bearing  539  to move in the direction of the right guide  536  and with low friction. The right carriage  531  may comprise an optional left rear support  544  and an optional left front support  556 , which may comprise a rotary member, a wheel, roller bearing, ball bearing, a bushing, and the like. The right bearing  539  and the optional left rear support  544  and optional left front support  556  help to support the force of the rider&#39;s right foot on the right carriage  531 . 
     The rider&#39;s right foot may be supported on the right carriage  531  with a right foot support  530 . The right foot support  530  may cover all or a portion of the rider&#39;s right foot. The rider&#39;s right foot may be attached to the right carriage  531  or to the right foot support  530  with straps, clips, Velcro, raised surfaces, molded surfaces, and the like. In the illustrative embodiment of  FIG. 5A , the right foot support  530  comprises a boot or sock, where the front portion of the boot or sock near the ball of the foot and toes is affixed  532  to the right carriage  531 . The right foot support  530  may be removably attached to the right carriage  531 . The rear portion  558  of the boot or sock near the heel of the foot may be unaffixed. The right foot support  530  may be removably attached to the right carriage  531  using Velcro, or any other convenient means that resists tangential forces, and can be easily removed if the rider needs to quickly remove his foot, such as if the SUP capsizes. 
     Forward translation of the right carriage  531  by the rider&#39;s right foot causes a right paddle blade to translate forward.  FIG. 5A  provides two right paddle blades, a forward right paddle blade  546  and a rear right paddle blade  547 ; although, there may be only one right paddle blade, there may be more than two right paddle blades, or there may be a right rotating wheel comprising a plurality of right paddle blades. 
     In  FIG. 5A , the forward right paddle blade  546  is able to rotate relative to the right carriage  531  about the edge  550 . The rear right paddle blade  547  is able to rotate relative to the right carriage  531  about the edge  551 . The right paddle blades  546  and  547  may rotate freely in a clockwise sense about the edges  550  and  551 , respectively, when the right carriage  531  translates forward in a recovery phase and the water  501  pushes backward against the right paddle blades  546  and  547 . The right paddle blades  546  and  547  may rotate freely in a counter-clockwise sense about the edges  550  and  551 , respectively, when the right carriage  531  translates backward in a thrust phase and the water  501  pushes forward against the right paddle blades  546  and  547 . However, once the right paddle blades  546  and  547  rotate CCW to a mostly downward orientation, as they are shown in  FIG. 5A , the right paddle blades typically are prevented from rotating further, for example employing a detent, such that further backward translation of the right carriage  531  causes the right paddle blades  546  and  547  to create forward thrust pushing against the water  501 . 
     A paddle-activating member, such as the left rear support  544  or left front support  556 , attached to the right carriage  531 , may cause one or both the right paddle blades  546  and  547  to rotate. For example, the left rear support  544  may be a paddle-activating member, and may comprise a wheel or a sector of a wheel, that when it rotates, it turns an axel that is attached to the edge  551  of the right rear paddle blade  547 , causing the right rear paddle blade  547  also to rotate. The paddle-activating member may also be a different wheel or sector of a wheel that is not shown, that causes one or more of the right paddle blades  546  and  547  to rotate when the right carriage  531  translates relative to the mounting structure  567 . Between the paddle-activating member and the right paddle blades  546  and  547  there may also be gears, cables, a transmission, and the like that give mechanical advantage to the paddle-activating member, or that changes the rate or direction that the right paddle blades  546  and  547  rotate as the right carriage  531  translates. 
     In  FIG. 5A , the left guide  540  is fastened to the mounting structure  567  with a front fastener  541  and a rear fastener  542 . The left guide  540  comprises a left bearing  543 . The left bearing  543  is attached to a left carriage  534  on which the rider&#39;s left foot may be placed. The left bearing  543  may comprise a rotary member, a wheel, roller bearing, ball bearing, a bushing, and the like, which allows the left bearing  543  to move in the direction of the left guide  540  and with low friction. The left carriage  534  may comprise an optional right rear support  545  and an optional right front support  557 , which may comprise a rotary member, a wheel, roller bearing, ball bearing, a bushing, and the like. The left bearing  543  and the optional right rear support  545  and optional right front support  557  help to support the force of the rider&#39;s left foot on the left carriage  534 . 
     The rider&#39;s left foot may be supported on the left carriage  534  with a left foot support  533 . The left foot support  533  may cover all or a portion of the rider&#39;s left foot. The rider&#39;s left foot may be attached to the left carriage  534  or to the left foot support  533  with straps, clips, Velcro, raised surfaces, molded surfaces, and the like. In the illustrative embodiment of  FIG. 5A , the left foot support  533  comprises a boot or sock, where the front portion of the boot or sock near the ball of the foot and toes is affixed  535  to the left carriage  534 . Similar to the right side, the rear portion of the boot or sock near the heel of the foot may be unaffixed. The left foot support  533  may be removably attached to the left carriage  534 . The left foot support  533  may be removably attached to the left carriage  534  using Velcro, or any other convenient means that resists tangential forces, and can be easily removed if the rider needs to quickly remove his foot, such as if the SUP capsizes. 
     Forward translation of the left carriage  534  by the rider&#39;s left foot causes a paddle blade to translate forward.  FIG. 5A  provides two left paddle blades, a forward left paddle blade  548  and a rear left paddle blade  549 ; although, there may be only one left paddle blade, there may be more than two left paddle blades, or there may be a left rotating wheel comprising a plurality of left paddle blades. 
     In  FIG. 5A , the forward left paddle blade  548  is able to rotate relative to the left carriage  534  about the edge  552 . The rear left paddle blade  549  is able to rotate relative to the left carriage  534  about the edge  553 . The left paddle blades  548  and  549  may rotate freely in a clockwise sense about the edges  552  and  553 , respectively, until they are mostly aligned with the surface of the SUP  500 , as they are shown in  FIG. 5A , when the left carriage  534  translates forward in a recovery phase and the water  501  pushes backward against the left paddle blades  548  and  549 . The left paddle blades  548  and  549  may rotate freely in a counter-clockwise sense about the edges  552  and  553 , respectively, when the left carriage  534  translates backward in a thrust phase and the water  501  pushes forward against the left paddle blades  548  and  549 . However, once the left paddle blades  548  and  549  rotate CCW to a mostly downward orientation, the left paddle blades typically are prevented from rotating further, for example employing a detent, such that further backward translation of the left carriage  534  causes the left paddle blades  548  and  549  to create forward thrust pushing against the water  501 . 
     A paddle-activating member, such as the right rear support  545  or right front support  556 , attached to the left carriage  534 , may cause one or both left paddle blades  548  and  549  to rotate. For example, the right rear support  545  may be a paddle-activating member, and may comprise a wheel or a sector of a wheel, that when it rotates, it turns an axel that is attached to the edge  553  of left rear paddle blade  549 , causing the left rear paddle blade  549  also to rotate. The paddle-activating member may also be a different wheel or sector of a wheel that is not shown, that causes one or more of the left paddle blades  548  and  549  to rotate when the left carriage  534  translates relative to the mounting structure  567 . Between the paddle-activating member and the left paddle blades  548  and  549  there may also be gears, cables, a transmission, and the like that give mechanical advantage to the paddle-activating member, or that changes the rate or direction that the left paddle blades  548  and  549  rotate as the left carriage  534  translates. 
     The turning of the handlebar  502  with the shaft  559  about the rotary joint  504  may cause the rudder  518  to turn the SUP  500 . Moving the right  503 A or left  503 B levers may also cause the rudder  518  to turn the SUP  500 . To cause the rudder  518  to turn, the handlebar  502  or the levers  503 A and  503 B are mechanically or electrically connected to the rudder  518 . Typical mechanical connections include a wire, cable, Bowden cable, flexible or rigid linkage, and the like, such as described for  FIG. 1A . Typical electrical connections include a rotary or linear sensor that senses a control signal and sends the control signal to an actuator, such as a rudder, brake, or paddle actuator. The control signal may be sent using wires or wirelessly, such as by Blue Tooth, RF, and the like. As described previously, an electrical system may be used in place of any mechanical structure described in this specification that provides movement of a cable or linkage to alter the position mechanically of a turnable rudder, a braking fin, or paddle blade. 
     In  FIG. 5A , Bowden cables are shown controlling the turning of the rudder  518 . The Bowden cable  525  is shown positioned along the top right portion of the SUP  500 , and then wraps around the rear portion of the SUP  500  as shown by the Bowden cable portion  526 . The Bowden cable tendon  524  is attached to a fin lever (similar to the cam  436  of FIG.  4 C). When the Bowden cable tendon  524  is translated, typically by turning the handlebars  502  or by moving the handlebar lever  503 A, the fin lever provides a connection point and mechanical advantage to help rotate the fin  518  about the rotary fin joint with the axis  520  relative to the fin mount  521  (similar to the rotary joint  426  of the rudder  423  and rudder bracket  433  of  FIG. 4C ). Similarly, the Bowden cable  528  is shown positioned along the top left portion of the SUP  500 , and then wraps around the rear portion of the SUP  500  as shown by the Bowden cable portion  529 . The Bowden cable tendon  527  is attached to a fin lever (similar to the cam  436  of  FIG. 4C ). When the Bowden cable tendon  527  is translated, typically by turning the handlebars  502  or by moving the handlebar lever  503 B, the fin lever provides a connection point and mechanical advantage to help rotate the fin  518  about the rotary fin joint with the axis  520  relative to the fin mount  521  (similar to the rotary joint  426  of the rudder  423  and rudder bracket  433  of  FIG. 4C ). 
       FIG. 5B  is a perspective view that provides exemplary embodiments for cams, gears, or wheels that control the position of paddle blades. A cam  560  may be associated with a wheel  544 , such that when the wheel  544  moves toward the rear of the SUP  500 , the cam  560  translates to the rear of the SUP  500 . Translation of the cam  560  to the rear of the SUP  500  causes it to rotate CCW  563  relative to a stationary element  561  with which it is rotationally engaged. The stationary element  561  may be a portion of the mounting structure  567  or a portion of the SUP  500 , such as the top surface. The cam  560  may rotationally engage with the stationary element  561  due to friction, gear teeth, cables, and the like. For illustrative purposes, the cam  560  is shown to be a sector of a disc, where the angle of the sector is selected based on the desired engagement properties. The larger the sector angle, the longer the cam  560  will remain engaged with the stationary element  561  during translation. The cam may also be a worm gear or other engagement system that remains engaged for a desired angle of rotation and then disengages, slips, rotates freely, and the like. As illustrated, after the cam  560  rotates a desired amount, further translation of the cam  560  to the rear of the SUP  500  will not cause it to additionally rotate CCW, since it is no longer rotationally engaged. Rather, the corner of the cam  560  will just drag along the stationary element  561 . 
     The cam  560  is shown attached to the rotation coupler  551 , which is attached to the paddle blade  547 . The rotation coupler  551  may comprise a rigid or flexible axel, may comprise one or more linkages, one or more gears, one or more cables, a transmission system, and the like. In  FIG. 5B , the rotation coupler  551  is shown for illustration purposes as a rigid axel. For clarity of the figure, the associated support structure for the cam  560 , the rotation coupler  551 , and the paddle blade  547  are not shown. When the cam  560  rotates CCW  563 , the paddle blade  547  also rotates CCW  564  due to the rotation coupler  551 . It is intended that when the right carriage  531  is translated backward  562  by the rider&#39;s right foot, i.e., the thrust phase, the cam  560  will cause the paddle blade  547  to enter the water  501  and remain in an activated position which is typically a substantially vertical orientation, even when there is further backward translation of the right carriage  531 . A rotation limiter  570  may be used to physically prevent the cam  560  from rotating further CCW. Alternatively, the rotation coupler  551  or the paddle blade  547  may include limiters that prevent the paddle blade  547  from rotating CCW substantially past the activated position. Accordingly, further translation backward of the right carriage  531  causes the paddle blade  547  to apply pressure against the water  501 , providing forward thrust to the SUP  500 . 
       FIG. 5C  provides a perspective view of the exemplary embodiment of  FIG. 5B  in a second state. The cam  560  may be associated with the wheel  544 , such that when the wheel  544  moves toward the front of the SUP  500 , the cam  560  translates toward the front of the SUP  500 . Translation of the cam  560  toward the front of the SUP  500  causes it to rotate CW  566  relative to the stationary element  561  with which it is rotationally engaged. As illustrated, after the cam  560  rotates a desired amount, further translation of the cam  560  toward the front of the SUP  500  will not cause it to additionally rotate CW, since it is no longer rotationally engaged. Rather, the corner of the cam  560  will just drag along the stationary element  561  without causing further rotation. 
     When the cam  560  rotates CW  566 , the paddle blade  547  also rotates CW  567  due to the rotation coupler  551 . It is intended that when the right carriage  531  is translated forward  565  by the rider&#39;s right foot, i.e., the recovery phase, the cam  560  will cause the paddle blade  547  to exit the water  501  and remain in an inactivated position which is typically a substantially horizontal orientation, even when there is further forward translation of the right carriage  531 . Accordingly, further translation forward of the right carriage  531  does not cause the paddle blade  547  to apply pressure against the water  501 , so no reverse thrust or resistance to movement along the water  501  is provided to the SUP  500 . 
     Although  FIGS. 5B and 5C  have been described for the right rear paddle blade  547 , the right front paddle blade  546 , left rear paddle blade  549 , and left front paddle blade  548  may also have similar cams ( 559 ,  571 ,  572 , respectively) and detents ( 552 ,  523 ,  519 , respectively). 
     The useful embodiment of  FIG. 5A  may employ the illustrative embodiment of the braking system employing a Bowden cable  413 . The tendon  440  of the Bowden cable  413  is attached to the brake fin lever  442  of the brake fin  401  at the location  441 . One of the handlebar levers  503  (or the brake lever  412  of  FIG. 4A ), or another mechanical or electrical control, may cause the tendon  440  to retract in the direction toward the sheath of the Bowden cable  413 . Retracting the tendon  440  in that direction causes the brake fin  401  to rotate CCW around the rotary joint  404  that is attached to the SUP  500  (or to the SUP  100  of  FIG. 4A ), typically to the underside of the rear portion of the SUP  500 , and extending the brake fin  401  farther down into the water, generating a resistive force. 
       FIG. 5D  provides an illustrative embodiment of a fastener assembly for securing the removable mounting structure  567  into a cavity  511  in the SUP  500 .  FIG. 5D  shows details of one illustrative embodiment of the fastener assembly connected to the mounting structure  567  and comprising one or more protruding members  516  and  517 , which may be hinged together at one end  574 . The protruding member may be a single piece with one or more sides that extend to apply pressure. When the mounting structure  567  is functionally positioned with the SUP  500 , the protruding members  516  and  517  of the fastener assembly extend into the cavity  511  of the SUP  500  for further positioning and fastening. In particular, the fastener assembly may comprise a control knob  512  with a ridge  513  for easily grasping that the rider may activate to secure the mounting structure  567  to the SUP  500 . For example, the rider may push or turn a portion of the control knob  512  to activate it for securing. In the figure, the control knob  512  is connected by a connecting member  514  to a cam  515 . The connecting member  514  may comprise a single shaft, multiple shafts, gears, cables, pulleys, a transmission, one or more links, and the like. In this illustrative embodiment, turning  573  the control knob  512  causes the cam  515  also to turn, which causes the protruding members  516  and  517  to be forced apart in the direction  572 , applying pressure to the sides of the cavity  511 , and securing the mounting structure  567  to the SUP  500 . The cam  515  may be any eccentric member that when rotated moves a portion of the cam  515  to alarger distance from the axis of rotation. The cam  515  may be circular, elliptical, oblong, or egg-shaped. In place of a cam  515  and protruding member  516  and  517 , the connecting member  514  may be threaded and screw into a threaded receiving member in the cavity  511 . 
       FIG. 5E  provides a side view of a low-profile strap  510  positioned against the surface of the SUP  500  in the water  501 . The strap  510  has streamlined leading  554  and trailing  555  edges to minimize water resistance. The low-profile strap may be used for any of straps  506 - 509 . 
       FIG. 6  is a perspective view of a useful embodiment of the invention. The SUP  600  is shown on water  601 . The handlebar  602  has right and left levers  603  that may control turning, braking, and the like. The handlebar  602  may not swivel, or it may swivel around rotary joint  604  relative to the handlebar base  605  that is attached to the SUP  600  or to a mounting structure  610 . The mounting structure  610  provides a rigid structure to which other elements may be attached to position such elements relative to each other and relative to the SUP  600 . 
     The mounting structure  610  may be permanently or removably attached to the SUP  600 . When the mounting structure  610  is removably attached to the SUP  600 , it allows a standard SUP  600  to be retrofit to comprise elements of the subject invention. The mounting structure  610  may fasten to a cavity  611  in the SUP  600 . Such a cavity  611  may also be used for hand carrying the SUP  600 .  FIG. 5D  shows details of one embodiment of a protruding member that extends into to the cavity  611  for positioning and fastening. In particular, as shown in  FIGS. 6 and 5D , the protruding member may comprise a control  512  that the rider may activate to secure the mounting structure  610  to the SUP  600 . The rider may turn a portion of the control  512  to activate it. 
     In  FIG. 6 , the mounting structure  610  is also shown strapped to the SUP  600 . Any convenient strap and strap termination method may be used. In  FIG. 6 , a forward strap  606  is fastened to the front-left portion of the mounting structure  610  by the strap end  607 . The forward strap  606  is then fastened to the front-right portion of the mounting structure  610  with a termination  622 . The termination  622  may comprise any convenient termination and tightening means, including but not limited to a buckle, a loop, Velcro®, and the like. Similarly, a rear strap  608  is fastened to the rear-left portion of the mounting structure  610  by the strap end  609 . The rear strap  608  is then fastened to the rear-right portion of the mounting structure  610  with a termination  624 . The termination  624  may comprise any convenient termination and tightening means, including but not limited to a buckle, a loop, Velcro®, and the like. 
     In  FIG. 6 , the mounting structure  610  has a right platform  612 . The rider may place their right foot on the right platform  612  and apply pressure using their weight. The right platform  612  may be mechanically connected to the mounting structure  610 . When it is connected, the right platform  612  may be rotatably connected to the mounting structure  610  with rotary joints  614  that cause the right platform  612  to rotate along the edge  613 . 
     The right platform  612  is connected to a right flipper  616  by a flipper-connecting member  615 . The right flipper  616  may comprise flipper structure similar to a common snorkeling or SCUBA-diving flipper. The flipper-connecting member  615  may be a rigid or flexible structure. In the illustrative embodiment of  FIG. 6 , the flipper-connecting member  615  is shown comprising a U-shaped connecting member that extends around the right side of the SUP  600 , so the right platform  612  may be above the SUP  600  and the right flipper may be below the SUP  600 , yet still remain connected. 
     When the rider steps down on the right platform  612 , the downward movement is translated by the flipper-connecting member  615  to the right flipper  616 , causing the right flipper  616  to translate downward through the water  601 . The physical structure of the right flipper  616  typically comprises a thicker, less flexible end, extending as it gradually narrows to a thin edge. The flipper-connecting member  615  connects near the thicker end of the right flipper  616 . So, when the thicker end of the right flipper  616  is translated downward, the right flipper  616  flexes as water  601  presses against it. As the right flipper  616  flexes, the portion of the right flipper  616  nearest the thin edge provides forward thrust, and propels the SUP  600  forward. In  FIG. 6 , the right flipper  616  is shown as it is starting a downward translation, where the right flipper  616  is curving upward near the thin edge. 
     In  FIG. 6 , the mounting structure  610  also has a left platform  617 . The rider may place their left foot on the left platform  617  and apply pressure using their weight. The left platform  617  may be mechanically connected to the mounting structure  610 . When it is connected, the left platform  617  may be rotatably connected to the mounting structure  610  with rotary joints  619  that cause the left platform  617  to rotate along the edge  618 . 
     The left platform  617  is connected to a left flipper  621  by a flipper-connecting member  620 . The left flipper  621  may comprise flipper structure similar to a common snorkeling or SCUBA-diving flipper. The flipper-connecting member  620  may be a rigid or flexible structure. In the illustrative embodiment of  FIG. 6 , the flipper-connecting member  620  is shown comprising a U-shaped connecting member that extends around the left side of the SUP  600 , so the left platform  617  may be above the SUP  600  and the left flipper may be below the SUP  600 , yet still remain connected. 
     When the rider steps down on the left platform  617 , the downward movement is translated by the flipper-connecting member  620  to the left flipper  621 , causing the left flipper  621  to translate downward through the water  601 . The physical structure of the left flipper  621  typically comprises a thicker, less flexible end, extending as it gradually narrows to a thin edge. The flipper-connecting member  620  connects near the thicker end of the left flipper  621 . So, when the thicker end of the left flipper  621  is translated downward, the flipper  621  flexes as water  601  presses against it. As the left flipper  621  flexes, the portion of the left flipper  621  nearest the thin edge provides forward thrust, and propels the SUP  600  forward. In  FIG. 6 , the left flipper  621  is shown as it is starting an upward translation, where the flipper  616  is curving downward near the thin edge. 
     The right platform  612  may be connected to a left platform  617  with a platform-connecting system, such that when the rider translates the right platform  612  downward, the platform-connecting system causes the left platform  617  to translate upward. One example of a platform-connecting system comprises a pulley  626  supported  627  relative to the SUP  600 , where a cable  625  is connected to the right platform  612  and the left platform  617  and passes around a portion of the pulley  626 . Using this platform-connecting system, when the right platform  612  is all the way down, the left platform  617  will be as far as it can go up, and vice versa. The intention is that the rider may stand with their right foot on the right platform  612 , and their left foot on the left platform  617 , and using a walking motion of transferring their weight from one foot to the other, the platforms  612  and  617  will go up and down in an alternating fashion, where movement of each platform  612  and  617  generates forward thrust. 
     In  FIG. 6 , Bowden cables are shown controlling the turning of the rudder  632 . The Bowden cable  628  is shown positioned along the top right portion of the SUP  600 , and then wraps around the rear portion of the SUP  600 . The Bowden cable tendon  629  is attached to a fin lever  630 . When the Bowden cable tendon  629  is translated, typically by turning the handlebars  602  or by moving one of the handlebar levers  603 , the fin lever  630  provides a connection point and mechanical advantage to help rotate the fin  632  about the rotary fin joint  631  relative to the fin mount  633 . Similarly, the Bowden cable  634  is shown positioned along the top left portion of the SUP  600 , and then wraps around the rear portion of the SUP  600 . The Bowden cable tendon  635  is attached to a fin lever  636 . When the Bowden cable tendon  635  is translated, typically by turning the handlebars  602  or by moving one of the handlebar levers  603 , the fin lever  636  provides a connection point and mechanical advantage to help rotate the fin  632  about the rotary fin joint  631  relative to the fin mount  633 . 
       FIGS. 7A, 7B, and 7C  provide a side view, perspective view, and top view, respectively, of an illustrative embodiment of an SUP  700  comprising one or more flippers  711  to provide forward thrust.  FIGS. 7A-7C  are similar to  FIG. 6  in that a flipper provides thrust; however, instead of showing the foot platform connected to a mounting structure with a rotary joint, as shown in  FIG. 6 , here the connection is shown as a flexible cable or articulated link. Additionally, in  FIG. 7 , no mounting structure is shown; although, a mounting structure may be conveniently used. Instead, steering and thrust members are shown connected directly to the SUP  700 . 
       FIG. 7A  is a side view of a useful embodiment of the invention. The SUP  700  is shown on water  701 . The handlebar  702  has right and left levers  703  that may control turning, braking, and the like. The handlebar  702  may not swivel, or it may swivel around rotary joint  704  relative to the handlebar base  705  that is attached to the SUP  700 . 
       FIG. 7A  provides a foot platform  706 , however a plurality of platforms may be used. There may be a right and a left platform. There may be platforms for a plurality of riders, such as a right and left front platform, and a right and left rear platform. 
     The rider may place their foot on the foot platform  706  and apply pressure using their weight. The foot platform  706  may be mechanically connected to the SUP  700 . When it is connected, the platform  706  may be connected to the SUP  700  with a thrust-connecting member  707  attached to the SUP  700  by the attachment member  708 . The thrust-connecting member  707  may be a flexible cable, a flexible tendon, a flexible rod, a rigid rod that is articulated, a rigid rod that is pinned at at least one end, and the like. 
     The foot platform  706  is connected to a flipper  711  by a flipper-connecting member  710 . The flipper  711  may comprise flipper structure similar to a common snorkeling or SCUBA-diving flipper. The flipper-connecting member  710  may be a rigid or flexible structure. In the illustrative embodiment of  FIG. 7 , the flipper-connecting member  710  is shown comprising a U-shaped flipper-connecting member that extends around the right side of the SUP  700 , so the foot platform  706  may be above the SUP  700  and the right flipper may be below the SUP  700 , yet still remain connected. 
     When the rider steps down on the foot platform  706 , the downward movement is transferred by the flipper-connecting member  710  to the flipper  711 , causing the flipper  711  to translate downward through the water  701 . The physical structure of the flipper  711  typically comprises a thicker, less flexible end, extending as it gradually narrows to a thin edge  712 . The flipper-connecting member  710  connects near the thicker end of the flipper  711 . So, when the thicker end of the flipper  711  is translated downward, the flipper  711  flexes as water  701  presses against it. As the flipper  711  flexes, the portion of the flipper  711  nearest the thin edge  712  provides forward thrust  713 , and propels the SUP  700  forward. In  FIG. 7 , the flipper  711  is shown as it is starting a downward translation, where the flipper  711  is curving upward near the thin edge  712 . 
     A foot support  709  is attached to the foot platform  706 . The foot support  709  is used to secure the rider&#39;s foot to the foot platform  706 . The foot support  709  may include a cavity like the boot portion of a snorkeling or SCUBA-diving flipper. The foot support  709  may include a Velcro strap to help secure the rider&#39;s foot. The foot support  709  may include a shoe or boot, which may include a Velcro strap to help secure the rider&#39;s foot in the shoe or boot, or which may secure the shoe or boot to the foot platform  706 . The foot support  709  may include an adjustable clam-like structure that is adjusted with a ratcheting mechanism to provide a snug support of the rider&#39;s foot. The foot support  709  may include a boot similar to a snow ski boot, which may have adjustable buckles or straps. The shoe or boot may have snap release that disengages from the foot platform  706 , such as if the rider where to tip over the SUP  700  and need to separate from the SUP  700 . 
     The thrust-connecting member  707  allows the rider to move their foot up and down. When the thrust-connecting member  707  is a flexible cable, the rider can also move their foot rearward, and forward until the cable is fully extended. When the thrust-connecting member  707  is a flexible cable, the intention is that the rider may more freely walk around on the SUP and direct the flipper  711  attached to the foot platform  706  to provide thrust in a variety of directions, where the thrust is transferred from the flipper  711  to the SUP  700  at the attachment member  708  when the cable is fully extended. The cable may also provide the function of a leash connecting the rider to the SUP  700 . When the rider&#39;s foot is firmly secured to the foot platform  706 , and the cable is fully extended, both lifting up and pressing down of the rider&#39;s foot may generate thrust in the direction the rider&#39;s foot is pointing. 
       FIG. 7B  provides a perspective view of the embodiment of  FIG. 7A . However, in  FIG. 7B , the flipper-connecting member  719  is shown comprising a plurality of link portions. The number of link portions may vary, as may the angles connecting them. The link portions may be straight or curved. In the illustrative embodiment of  FIG. 7B , the flipper-connecting member  719  comprises four link portions arranged to position the foot platform  706  at a desired location relative to the flipper  711 . In the illustrative embodiment of  FIG. 7B , the foot platform  706  is connected to a first link portion  720  that extends to the side of the foot platform  706  and extends out past the right edge of the SUP  700 . The first link portion  720  is connected at substantially 90 degrees to the second link portion  721  which extends substantially forward or backward. The second link portion  721  is connected at substantially 90 degrees to the third link portion  722  that extends downward toward the water. The third link portion  722  is connected at substantially 90 degrees to the fourth link portion  723  that extends back under the SUP and connects to the flipper  711 . 
     The flipper  711  is also shown with an optional ridge  717  that may be used to provide bending reinforcement to the flipper  711 . The dimensions, design, and material of the ridge  717  may be selected to provide a desire curvature versus speed of up and down translation of the flipper  711 . Such a ridge may be used on any of the other flippers, paddles and fins of the illustrative embodiments. 
     The flipper  621  of  FIG. 6 , the flipper  711  of  FIGS. 7A-7C , and the flipper  800  of  FIG. 8  may be made of rubber, plastic, composite, common flipper materials, or any convenient material that is compatible with water. Typically, the flippers are made from a flexible material and/or the flippers are allowed to rotate about one end. 
       FIG. 7C  provides a top view of the embodiment of  FIG. 7A . However, in  FIG. 7C , the flipper-connecting member  724  is shown comprising a U-shaped link. The dimensions of the flipper-connecting member  724  are selected to place the center of force  718  from the foot platform  706  at the desired location relative to the flipper  711 . For instance, the center of force  718  may be positioned over the flipper  711  so the rider does not perceive an uncomfortable force on their ankle. As the center of force  718  is moved rearward, more of the force is perceived by the rider to be exerted by their heel. Similarly, as the center of force  718  is moved forward, more of the force is perceived by the rider to be exerted by their toe. 
     In  FIGS. 7B and 7C , the outline of the SUP  700  is not intended to limit the placement of the foot platform  706 , the thrust-connecting members, the flipper-connecting members, and the flippers, and the like. 
       FIGS. 8A and 8B  provide perspective views of a flipper  800  with a connected end  801  and a free end  802 .  FIG. 8A  provides the flipper  800  in a first orientation relative to a flipper-connecting member  803 .  FIG. 8B  provides the flipper  800  in a second orientation relative to the flipper-connecting member  803 . The flipper  800  may be flexible or substantially inflexible. The assembly of  FIGS. 8A and 8B  provides that thrust is primarily generated when the rider presses down on a foot platform connected to the flipper-connecting member  803 ; but when the rider lifts their foot, they feel relatively little resistance. The flipper-connecting member  803  of  FIGS. 8A and 8B  may conveniently replace the flipper  616  and be connected to the flipper-connecting member  615  of  FIG. 6 , replace the flipper  621  and be connected to the flipper-connecting member  615  of  FIG. 6 , or replace the flipper  711  and be connected to the flipper-connecting member  710  of  FIG. 7A , the flipper-connecting member  719  of  FIG. 7B , or the flipper-connecting member  724  of  FIG. 7C . 
     In  FIG. 8A , when the rider causes the flipper-connecting member  803  to translate downward  804 , such as when the rider puts weight on an associated foot platform, water applies a force against the bottom surface of the flipper  800 , causing it to rotate CW relative to the flipper-connecting member  803  and about the rotary joint  810  near the connected end  801 , until the rotation stopper  805  on the flipper  800  contacts the detent  806  on the flipper-connecting member  803 , preventing further rotation. During CW rotation, the rotation may be free without resistance, or rotary resistance may be added, but typically resistance is added only when the flipper  800  is flexible. When further rotation is prevented, further downward translation  804  of the flipper-connecting member  803  provides forward thrust generated from the flipper  800  and transmitted to the SUP via the flipper-connecting member  803 . 
       FIG. 8B  provides the case where the flipper-connecting member  803  is lifted. In this case, the flipper  800  rotates CCW  809  about the rotary joint  810 , unless the rotation stopper  805  on the flipper  800  contacts the detent  807  on the flipper-connecting member  803 , preventing further rotation. During CCW rotation, typically the rotation is free without resistance; although, rotary resistance may be added. When the rotation is free and without resistance, it allows the rider to easily lift their foot, so they don&#39;t need to work their quadriceps much during the recovery phase. 
     After the flipper  800  is lifted and there is little or no vertical movement of the flipper-connecting member  803  as the SUP is gliding, the flipper  800  will freely rotate CW to a substantially horizontal orientation due to the force of the water. It may be desirable to make the flipper  800  from a buoyant material to cause the flipper  800  to more quickly rotate to a substantially horizontal orientation to reduce drag. Otherwise, once the SUP slows its glide, the flipper  800  may start rotating CCW towards a more vertical orientation due to its weight and provide more drag, in addition to not being in a good orientation to initiate the next downward thrust phase. 
     Further general discussion of the embodiments of  FIGS. 7A-7C  and  FIGS. 8A-8B  follows: 
     1. The flipper is typically positioned under the foot so the center of force from the flipper passes through the center of the foot, so there is no twisting of the foot. 
     2. The connecting member from the shoe platform to the flipper is streamlined to pass through water. The connecting member may have some springiness to it. 
     3A. The side bar that rotates relative to the flipper is prevented by a detent (1) from rotating substantially past horizontal when pushing down with the foot. When lifting the foot, the flipper may rotate downward freely, or there may be torsional resistance, or there may be another detent (2) that prevents the flipper from angling down too far. That is, the rider may feel some resistance upon raising their foot, which exercises the quad. 
     3B. Alternately, the side bar may not rotate relative to the flipper, and the flipper flexes to provide thrust. 
     3C. Alternately, the side bar may deflect torsionally when lifting the foot or/and pressing down. 
     4A. The side bar may detach from the shoe/foot platform. 
     4B. The shoe platform may detach from the shoe. For example, clips, straps, Velcro, and the like, may be used. 
     5. Right and left SUP flippers are best used together. 
       FIG. 9A  is a perspective view of an illustrative embodiment of a plurality of SUP members  900  and  905 , each comprising one or more thrust actuators  902 ,  903 ,  904 ,  906 ,  907 , and  908  for providing forward thrust. In  FIG. 9A , no mounting structure or breaking assembly is shown; although, a mounting structure and breaking assembly may be conveniently used. Instead of an optional mounting structure, foot supports  912  and  913 , as well as thrust actuators  902 ,  903 ,  904 ,  906 ,  907 , and  908 , are shown connected directly to the SUPs  900  and  905 . 
     The SUP  900  is shown floating on water  901 . The rider/user  914  shown for simplicity as a stick figure is representative of a mammal, such as a human, having head  927 , neck  926 , shoulders  923 , right humerus  924 , right forearm  928 , with their right hand holding the right handle  930 , and further having left humerus  925 , left forearm  929 , with their left hand holding left handle  933 , and further having torso  922 , hips  918 , right thigh  917 , right shin  916 , and right foot  915  on right foot support  912 , and further having left thigh  921 , left thin  920 , and left foot  919  on left foot support  913 . 
     Attached to the bottom of right SUP  900  is at least one thrust actuator. Three thrust actuators are shown, including a front thrust actuator  902 , a middle thrust actuator  903 , and a rear thrust actuator  904 . Similarly, attached to the bottom of left SUP  905  is at least one thrust actuator. Three thrust actuators are shown, including a front thrust actuator  906 , a middle thrust actuator  907 , and a rear thrust actuator  908 . An example suitable thrust actuator is further provided in  FIGS. 9B-9D . 
     The extension structure  931  connects the right handle  930  to right balance float  932 . Similarly, the extension structure  934  connects the left handle  933  to left balance float  935 . The rider  914  may hold the handles  930  and  932  to help remain balanced by applying force on the handles  930  and  932  in the direction of the balance floats  932  and  935 . The balance floats  932  and  935  may be hollow members, low-density members such as foam members, inflatable member such as inflatable balls, or any other suitable buoyant object to help the rider  914  remain balanced. 
     One or both of the handles  930  and  932  may comprise steering and/or braking controls (not shown). Such controls may include a rotary control, a squeeze control, a tilt control, a button control, a pressure control, a twist control, a lever, a controller such as found on a video game control input, and the like. The steering and/or breaking controls may wirelessly communicate with, or otherwise affect, an associated steering and/or braking actuator. A single steering and/or braking control may control the steering and/or braking actuator for either or both SUPs  900  and  905 . A wireless right steering/braking actuator  912  is provided for SUP  900 , and a wireless left steering/braking actuator  910  is provided for SUP  905 . The wireless right steering/braking actuator  912  may control the right steering fin  911  and/or the left steering fin  909 . Similarly, the wireless left steering/braking actuator  910  may control the left steering fin  909  and/or the right steering fin  911 . A braking actuator is not explicitly shown, but may take any form, including a braking fin actuator assembly such as provided by  FIGS. 4A-4D . 
       FIG. 9B  is a perspective view of the thrust actuator  942 , such as may be used in  FIG. 9A . The thrust actuator  942  is collapsible. The thrust actuator  942  typically has two rigid surfaces connected by two flexible surfaces. In  FIG. 9B , the thrust actuator  942  is fastened to the bottom surface of an SUP by a first rigid surface  941 . The rigid surface  941  is connected to a second rigid surface  937  by flexible sides  936 . The first rigid surface  941  may also be connected to the second rigid surface  937  by a hinge  940 . The flexible sides may include bellow folds or other structure to facilitate easy, complete, and repeatable collapsing of the second rigid surface  937  against the first rigid surface  941 . If the thrust actuator is substantially wedge shaped, then when the SUP  900  is traveling through a fluid, such as water, in the direction of the hinged end  940  of the thrust actuator  942 , the second rigid surface  937  will collapse on its own against the first rigid surface  941 , such that the thrust actuator provides little resistance to travel. Conversely, if the SUP  900  is traveling in the other direction, i.e., toward the cavity opening  943  and away from the hinged end  940 , then the opening  943  will remain open and capture fluid, providing a resistive force to travel in that direction. Accordingly, as the rider  914  slides their foot  915  forward and their foot  919  backward (or vice versa), the SUP  900  will also slide forward and SUP  905  backward; however, due to the difference in forward/backward sliding resistances, SUP  900  will slide forward more than SUP  905  will slide backward, where SUP  900  is essentially pushing forward against the resistive force provided by SUP  905 . Thus, as the rider  914  repeatedly slides their feet forward and backward, but 180 degrees out of phase, the rider  914  will achieve net forward travel, i.e., in the direction of the hinges  940  and away from the cavities  943 . 
       FIG. 9C  is a perspective view of the collapsed thrust actuator of  FIG. 9B . 
       FIG. 9D  is an end view of a partially collapsed thrust actuator. Although not required,  FIG. 9D  provides that the right and left flexible sides  936  comprise a bellows fold. The bellows fold may comprise somewhat rigid slats connected by flexible material, much like an accordion. The flexible material may be plastic, vinyl, fabric, polypropylene, nylon, polyurethane laminate (PUL), and the like. Typically, the material will fold without much force required, so the thrust actuator easily collapses, and the material should provide some resistance to fluid flowing through it to generate a resistive force when the SUP, to which the thrust actuator is attached, is pushed backwards. 
       FIG. 9E  is a perspective view of means for securing a foot to a foot support. A foot attached to leg portion  944  is inserted into a foot holder  945 . The foot holder  945  may have structure similar to a laced show, a slip-on shoe, a waterski boot, which may be adjustable, a water sock, a sandal, and the like. The foot holder  945  comprises a holder base  946  that may be removably fastened to the foot support  950 . In  FIG. 9E , the holder base  946  is flexible about to be removably fastened by the fastening surface  948  near the toe end  947  to a mating fastening surface  949  on the foot support  950 . One suitable fastening surface  948  is loop Velcro, and a suitable mating fastening surface  949  is hook Velcro. The loop and hook Velcro surfaces may be swapped. In  FIG. 9E , the toe end  947  of the holder base  946  may comprise loop Velcro  948 , and it may be removably mated to hook Velcro  949  on the foot support  950 . The holder base  946  may be any flexible material, such as rubber, neoprene, fabric, and the like. The holder base  946  may be attached to the foot support  950  at any point, but is typically fastened near the ball of the foot or toe end of the holder base to make it easy for the rider  914  to lift their heel, like a Nordic snow skier. The holder base  946  may be removably attached to the foot support  950  using any convenient means, including Velcro, a snow-ski binding, a snap, and the like. The removable attachment should provide transfer of tangential forces, but easily separate when vertical forces are applied, such as if the rider falls from the SUP. 
       FIG. 9F  is a side view of the apparatus of  FIG. 9E , where the rider  914  has lifted their heel, such as when pushing rearward.  FIG. 9F  also provides the holder base  946  already removably fastened by fastening surface  948  to the fastening surface  949  of the foot support  950 . 
       FIG. 9G  is a top view of a steering control and actuator assembly. A foot at the end of the leg  944  is held by the foot holder  945  to the holder base  946 . The holder base  946  may rotate or pivot around the rotary joint  961 . When the holder base  946  rotates counter clockwise, as shown by the arrows  968  and  969 , the holder base pulls on one end  965  of a tendon of a Bowden cable with sheath  962 . One end  963  of the sheath  962  of the Bowden cable is attached to the SUP near the holder base  946 , and the other end  964  of the sheath  962  is attached to the SUP near the steering rudder  911 . The other end  966  of the tendon of the Bowden cable exits the end  964  of the sheath and is attached to a rudder attachment  967 . Accordingly, when the holder base rotates counter clockwise, the steering rudder  911  rotates clockwise about the rotary joint  963 , as shown by the arrows  970  and  971 . So, the rider  914  may slide an SUP forward and backward, and may also turn their foot to cause the SUP also to turn.  FIG. 9G  is a mechanical steering controller and actuator; however, the Bowden cable may be replaced by a rotation sensor wirelessly communicating a rotation signal to a rotation actuator functionally related to a steering rudder, such as described in  FIG. 9A . 
       FIG. 9H  is a front end view of one embodiment of SUPs  900  and  905 , where the curvature of the bottoms of the SUPs  900  and  905  are substantially symmetrically curved. Legs  944  and  951  are held by foot holders  945  and  952 , respectively, which are supported by holder bases  946  and  953 , respectively, which are removably attached to SUPs  900  and  905  with cross sections  947  and  954 , respectively. 
       FIG. 9I  is a front end view of another embodiment of SUPs  900  and  905 , where the curvature of the bottoms of the SUPs  900  and  905  are not symmetrically curved. Instead, the depth of the SUPs  900  and  905  are deeper in one area. Legs  944  and  951  are held by foot holders  945  and  952 , respectively, which are supported by holder bases  946  and  953 , respectively, which are removably attached to SUPs  900  and  905  with cross sections  955  and  958 , respectively. Cross section  955  has a deeper portion  957  and a shallower portion  956 , while cross section  958  has a deeper portion  960  and a shallower portion  959 . Having deeper and shallower portions can improve overall balance by providing more buoyant force where there is more weight load. 
       FIG. 9J  is a side view of one exemplary front end  961  of the SUPs  900  and  905 , showing an exemplary fluid/water level  962 . 
       FIG. 10A  is a side view of a useful embodiment of a thrust assembly. Such a thrust assembly may be substituted or combined with other thrust assemblies or actuators, such as the thrust actuators  902 ,  903 ,  904 ,  906 ,  907 , and  908 , of the SUPs  900  and  905  of  FIG. 9A . In the thrust assembly of  FIG. 10A , the rider&#39;s foot  1002  is resting on the foot support  1003 . Alternately, a foot holder  1002  is removably secured to the foot support  1003 , and the rider&#39;s foot is held by the foot holder  1002 . The foot support  1003  is flexible and may be attached to the SUP  1000  in a variety of ways. In  FIG. 10A , the foot support  1003  is attached at a first end to a rotary joint  1004 , which rotates relative to the mount  1005  which is firmly affixed to the SUP  1000  floating in fluid  1001 , such as fresh or salt water. The second end of the foot support  1003  is able to move relative to the SUP  1000 . In  FIG. 10A , in one example, the second end of the foot support  1003  is attached to a roller joint with axis  1007  and roller wheel  1006  that rolls relative to the SUP  1000 . Alternatively, the roller wheel may be replaced by a linear bearing or other convenient sliding joint. As shown in  FIG. 10B , when the rider stands on, or applies sufficient weight to, the foot support  1003 , it flexes down in the direction of the arrow  1011 , and one or more thrust paddles  1008  extend in the direction of the arrows  1012  through the paddle slots  1009  into the water past the bottom surface  1010  of the SUP  1000 . Typically, two SUPs are used by a rider: one SUP for each foot of the rider, where each SUP is configured according to  FIG. 10A . When the rider shifts their weight from one SUP to the other, they may apply a forward thrust force with the SUP supporting their weight, since the thrust paddles  1008  will be capable of applying a forward or rearward force against the water. When the rider applies a rearward force with one SUP, the other SUP that is not supporting the rider&#39;s weight will have thrust paddles  1008  retracted to the position provided by  FIG. 10A , and not providing a resistive force to forward gliding motion. The result is that the rider may, in effect, skate on the surface of the water, using a weight-shifting sliding technique similar to a Nordic snow skier. 
       FIG. 10C  is a side view of a useful embodiment of another thrust assembly. Such a thrust assembly may be substituted or combined with other thrust assemblies or actuators, such as the thrust actuators  902 ,  903 ,  904 ,  906 ,  907 , and  908 , of the SUPs  900  and  905  of  FIG. 9A , or the thrust assembly of  FIGS. 10A and 10B . In the thrust assembly of  FIG. 10C , the rider&#39;s foot  1017  is resting on the foot support  1018 . Alternately, a foot holder  1017  is removably secured to the foot support  1018 , and the rider&#39;s foot is held by the foot holder  1017 . The foot support  1018  may be attached to the SUP  1015  in a variety of ways. In  FIG. 10C , the foot support  1018  is supported relative to the surface of the SUP  1015  using springs  1019 . The SUP  1015  is floating in fluid  1016 , such as fresh or salt water. There is at least one thrust paddle  1025  with a rotary joint  1027  at one end capable of rotating relative to a mount  1026  which is firmly affixed to the SUP  1015 . Corresponding to each thrust paddle  1025  is a push rod  1023 . Each push rod  1023  has a rotary joint  1024  at one end capable of rotating relative to an associated thrust paddle  1025 , and another rotary joint  1022  at the other end of the push rod  1023  capable of rotating relative to an associated mount  1021  which is firmly affixed to the foot support  1018 .  FIG. 10C  shows the thrust paddles  1025  in their retracted position, which produces very little resistance to water flow past the SUP  1015 . As shown in  FIG. 10D , when the rider stands on, or applies sufficient weight to, the foot support  1018 , it translates down and compresses the springs  1019 , and one or more thrust paddles  1025  are forced by the push rods  1023  to rotate counter clockwise to an extended position, extending downward deeper into the water. In the extended position, a thrust paddle is capable of applying a force against the water supporting the SUP  1015  to direct the SUP  1015  forward or rearward. Typically, two SUPs are used by a rider: one SUP for each foot of the rider, where each SUP is configured according to  FIG. 10C . When the rider shifts their weight from one SUP to the other, they may apply a forward thrust force with the SUP supporting their weight, since the thrust paddles  1025  will be capable of applying a forward or rearward force against the water. When the rider applies a rearward force with one SUP, the other SUP that is not supporting the rider&#39;s weight will have thrust paddles  1025  retracted to the position provided by  FIG. 10C , and not providing a resistive force to forward gliding motion. The result is that the rider may, in effect, skate on the surface of the water, using a weight-shifting sliding technique similar to a Nordic snow skier. 
       FIG. 11A  is a side view of a useful embodiment of another thrust assembly. Such a thrust assembly may be substituted or combined with other thrust assemblies or actuators, such as the thrust actuators  902 ,  903 ,  904 ,  906 ,  907 , and  908 , of the SUPs  900  and  905  of  FIG. 9A , or the thrust assemblies of  FIGS. 10A-10D . In the thrust assembly of  FIG. 11A , the rider&#39;s foot  1108  is resting on the SUP  1100 . Alternately, a foot holder  1108  is removably secured to the SUP  1100 , and the rider&#39;s foot is held by the foot holder  1108 . The foot holder  1108  may be attached to the SUP  1100  in a variety of ways. The SUP  1100  is floating in fluid  1101 , such as fresh or salt water. There is at least one thrust paddle  1111  with a rotary joint  1112  capable of rotating relative to a mount  1113  which is firmly affixed to the SUP  1100 . Extending from each thrust paddle  1111  is a rocker arm  1109 . Each rocker arm  1109  has a rotary joint  1110  at one end capable of rotating relative to a tie rod  1107 . If there is more than one thrust paddle  1111 , the rocker arm  1109  of each thrust paddle  1111  will be forced to rotate in unison by the connecting tie rod  1107 .  FIG. 11A  shows the thrust paddles  1111  in their retracted position, which produces very little resistance to water flow past the SUP  1100 .  FIG. 11A  also provides a lever arm  1103  with handle  1102 . The lever arm  1103  has a rotary joint  1104  capable of rotating relative to a mount  1105  which is firmly affixed to the SUP  1100 . The lever arm  1103  also has a rotary joint  1106  capable of rotating relative to the tie rod  1107 . As shown in  FIG. 11B , when the rider pulls the lever arm  1103  toward them, the thrust paddles  1111  are forced by the tie rod  1107  to rotate counter clockwise to an extended position, extending downward deeper into the water. In the extended position, a thrust paddle is capable of applying a force against the water supporting the SUP  1100  to direct the SUP  1100  forward or rearward. Typically, two SUPs are used by a rider: one SUP for each foot of the rider, where each SUP is configured according to  FIG. 11A . When the rider shifts their weight from one SUP to the other, they may apply a forward thrust force with the SUP supporting their weight, since the thrust paddles  1111  will be capable of applying a forward or rearward force against the water. When the rider applies a rearward force with one SUP, the other SUP that is not supporting the rider&#39;s weight will have thrust paddles  1111  retracted to the position provided by  FIG. 11A , and not providing a resistive force to forward gliding motion. The result is that the rider may, in effect, skate on the surface of the water, using a weight-shifting sliding technique similar to a Nordic snow skier. 
       FIG. 11C  is a side view of a useful embodiment of another thrust assembly. Such a thrust assembly may be substituted or combined with other thrust assemblies or actuators, such as the thrust actuators  902 ,  903 ,  904 ,  906 ,  907 , and  908 , of the SUPs  900  and  905  of  FIG. 9A , or the thrust assemblies of  FIGS. 10A-10D  and  FIGS. 11A-11B . In the thrust assembly of  FIG. 11C , the rider&#39;s foot (not shown) may rest on top of the SUP  1114 . Alternately, a foot holder may be removably secured to the SUP  1114 , and the rider&#39;s foot may be held by the foot holder. The SUP  1114  is floating in fluid  1115 , such as fresh or salt water. There is at least one thrust paddle  1122  affixed to the paddle support  1121 .  FIG. 11C  also provides a lever arm  1117  with handle  1116 . The lever arm  1117  has a rotary joint  1124  capable of rotating relative to a mount  1125  which is firmly affixed to the SUP  1114 . The lever arm  1117  also has a rotary joint  1128  capable of allowing a tie rod  1118  to rotate relative to the lever arm  1117 . The tie rod  1118  has a rotary joint  1119  capable of rotating relative to a mount  1120  which is firmly affixed to the paddle support  1121 .  FIG. 11C  shows the thrust paddles  1122  in their retracted position, which produces very little resistance to water flow past the SUP  1114 . As shown in  FIG. 11D , when the rider pulls the lever arm  1117  toward them in the direction of the arrow  1126 , the tie rod  1118  forces the paddle support  1121  to force the thrust paddles  1122  to extend downward through the paddle slots  1123  in the direction of the arrows  1127  deeper into the water. In the extended position, a thrust paddle  1122  is capable of applying a force against the water supporting the SUP  1114  to direct the SUP  1114  forward or rearward. Typically, two SUPs are used by a rider: one SUP for each foot of the rider, where each SUP is configured according to  FIG. 11C . When the rider shifts their weight from one SUP to the other, they may apply a forward thrust force with the SUP supporting their weight, since the thrust paddles  1122  will be capable of applying a forward or rearward force against the water. When the rider applies a rearward force with one SUP, the other SUP that is not supporting the rider&#39;s weight will have thrust paddles  1122  retracted to the position provided by  FIG. 11C , and not providing a resistive force to forward gliding motion. The result is that the rider may, in effect, skate on the surface of the water, using a weight-shifting sliding technique similar to a Nordic snow skier. 
       FIG. 12A  is a side view of a useful embodiment of another thrust assembly. Such a thrust assembly may be substituted or combined with other thrust assemblies or actuators, such as the thrust actuators  902 ,  903 ,  904 ,  906 ,  907 , and  908 , of the SUPs  900  and  905  of  FIG. 9A , or the thrust assemblies of  FIGS. 10A-10D and 11A-11D . In the thrust assembly of  FIG. 12A , the rider&#39;s foot  1202  is resting on the SUP  1200 . Alternately, a foot holder  1202  is removably secured to the SUP  1200 , and the rider&#39;s foot is held by the foot holder  1202 . The foot holder  1202  may be attached to the SUP  1200  in a variety of ways. The SUP  1200  is floating in fluid  1201 , such as fresh or salt water. There is at least one thrust paddle  1203  with a rotary joint  1204  capable of rotating relative to a mount  1205  which is firmly affixed to the SUP  1200 . Positioned in functional relation to each thrust paddle  1203  is a limit-stop structure  1206  to prevent each thrust paddle  1203  from rotating past substantially extending straight down into the water during a forward-thrust phase.  FIG. 12A  shows the thrust paddles  1203  in their retracted position, which produces very little resistance to water flow past the SUP  1200 , where the orientation of each thrust paddle  1203  is determined by the flow of water which rotates the thrust paddles  1203  clockwise in the figure when the SUP  1200  is traveling to the right. As shown in  FIG. 12B , when the rider pushes the SUP  1200  rearward (i.e., to the left in the figure), the thrust paddles  1203  are forced by the water  1201  to rotate counter clockwise to an extended position against the limit-stop structures  1206 , extending downward deeper into the water. In the extended position, a thrust paddle  1203  is capable of applying a force against the water supporting the SUP  1200  to direct the SUP  1200  forward. Typically, two SUPs are used by a rider: one SUP for each foot of the rider, where each SUP is configured according to  FIG. 12A . When the rider applies a forward thrust force to a first SUP, the thrust paddles  1203  will rotate into the extended position and apply a rearward force against the water. The second SUP that is gliding forward will have its thrust paddles  1203  retracted by the force of the water to the retracted position as provided by  FIG. 12A , and not provide a material resistive force to forward motion. The rider then applies a forward thrust force to the second SUP while the first SUP is gliding forward. The result is that the rider may, in effect, skate on the surface of the water, using an alternating-foot sliding technique, similar to a Nordic snow skier. 
       FIG. 12C  is a side view of a useful embodiment of another thrust assembly. Such a thrust assembly may be substituted or combined with other thrust assemblies or actuators, such as the thrust actuators  902 ,  903 ,  904 ,  906 ,  907 , and  908 , of the SUPs  900  and  905  of  FIG. 9A , or the thrust assemblies of  FIGS. 10A-10D, 11A-11D, and 12A-12B . In the thrust assembly of  FIG. 12C , the rider&#39;s foot  1209  is resting on the SUP  1207 . Alternately, a foot holder  1209  is removably secured to the SUP  1207 , and the rider&#39;s foot is held by the foot holder  1209 . The foot holder  1209  may be attached to the SUP  1207  in a variety of ways. The SUP  1207  is floating in fluid  1208 , such as fresh or salt water. The SUP  1207  is attached to a paddle float  1215  which keeps the thrust paddles  1221  attached to it at a desired depth, regardless of the weight of the rider. The paddle float  1215  may be attached to the SUP  1207  in a variety of ways. In  FIGS. 12C and 12D , the paddle float  1215  is connected to the SUP  1207  in an articulated manner by a front tie rod  1210 . The front tie rod  1210  has a rotary joint  1214  at the paddle-float end that rotates relative to the mount  1213  which is firmly affixed to the paddle float  1215 . The front tie rod  1210  also has a rotary joint  1212  at the SUP end that rotates relative to the mount  1211  which is firmly affixed to the SUP  1207 . Although optional, as shown in  FIGS. 12C and 12D  the paddle float  1215  is also connected to the SUP  1207  by a rear tie rod  1216 . The rear tie rod  1216  has a rotary joint  1220  at the paddle-float end that rotates relative to the mount  1219  which is firmly affixed to the paddle float  1215 . The rear tie rod  1216  also has a rotary joint  1218  at the SUP end that rotates relative to the mount  1217  which is firmly affixed to the SUP  1207 . Based on the articulated relationship between the SUP  1207  and the paddle float  1215 , the paddle float  1215  may float at a depth desired for the thrust paddles  1221 , independently from the depth that the SUP  1207  floats at, which depends on the weight of the rider. There is at least one thrust paddle  1221  with a rotary joint  1222  capable of rotating relative to a mount  1223  which is firmly affixed to the paddle float  1215 . Positioned in functional relation to each thrust paddle  1221  is a limit-stop structure  1224  to prevent each thrust paddle  1221  from rotating past substantially extending straight down into the water during a forward-thrust phase.  FIG. 12C  shows the thrust paddles  1221  in their retracted position, which produces very little resistance to water flow past the paddle float  1215  and the connected SUP  1207 , where the orientation of each thrust paddle  1221  is determined by the flow of water which rotates the thrust paddles  1221  clockwise in the figure when the paddle float  1215  and the connected SUP  1207  is traveling to the right. As shown in  FIG. 12D , when the rider pushes the SUP  1207  rearward (i.e., to the left in the figure), the paddle float  1215  also is pushed rearward by the tie rods  1210  and  1216 , and the thrust paddles  1221  are forced by the water  1208  to rotate counter clockwise to an extended position against the limit-stop structures  1224 , extending the thrust paddles  1221  downward deeper into the water. In the extended position, a thrust paddle  1221  is capable of applying a force against the water supporting the paddle float  1215 , which directs the paddle float  1215  and SUP  1207  forward. Typically, two SUPs are used by a rider: one SUP for each foot of the rider, where each SUP is configured according to  FIG. 12C . When the rider applies a forward thrust force to a first SUP, the thrust paddles  1221  will rotate into the extended position and apply a rearward force against the water. The second SUP that is gliding forward will have its thrust paddles  1221  retracted by the force of the water to the retracted position as provided by  FIG. 12C , and not provide a material resistive force to forward motion. The rider then applies a forward thrust force to the second SUP while the first SUP is gliding forward. The result is that the rider may, in effect, skate on the surface of the water, using an alternating-foot sliding technique, similar to a Nordic snow skier. 
     Note that in place of, or in addition to, thrust paddles  1221  affixed to the paddle float  1215 , other thrust actuators may be affixed to the paddle float  1215 , such as the thrust actuators  902 ,  903 ,  904 ,  906 ,  907 , and  908 , of the SUPs  900  and  905  of  FIG. 9A . In general, a thrust actuator that is capable of applying more force to the water in one direction than the opposite direction may be used. 
     For any of the illustrative embodiments, a thrust actuator may be located to the side of the SUP, under the SUP, partially to the side and partially under the SUP, partially to the side and partially above the SUP, or a portion inset into cavity in the SUP. 
       FIG. 13A  is a side view of a useful embodiment of another thrust assembly. Such a thrust assembly may be substituted or combined with other thrust assemblies or actuators, such as the thrust actuators  902 ,  903 ,  904 ,  906 ,  907 , and  908 , of the SUPs  900  and  905  of  FIG. 9A , or the thrust assemblies of  FIGS. 10A-10D, 11A-11D, and 12A-12D . In the thrust assembly of  FIG. 13A , the rider&#39;s foot  1305  is resting on the SUP  1300 . Alternately, a foot holder  1305  is removably secured to the SUP  1300 , and the rider&#39;s foot is held by the foot holder  1305 . The foot holder  1305  may be attached to the SUP  1300  in a variety of ways. The SUP  1300  is floating in fluid  1301 , such as fresh or salt water. There is at least one thrust paddle wheel  1311  with a rotary joint  1303  capable of rotating relative to a mount  1304  which is firmly affixed to the SUP  1300 . There are a plurality of thrust paddles  1302  affixed to each thrust paddle wheel  1311 , where the number of thrust paddles  1302  per thrust paddle wheel  1311  is typically at least four so that at least one thrust paddle  1302  will be in the water at all times. 
     A rotation-direction-limiting structure associated with each thrust paddle wheel  1311  prevents each thrust paddle wheel  1311  from rotating counter clockwise in the figure during a forward-thrust phase, but allows each thrust paddle wheel  1311  to rotate clockwise in the figure with little resistance.  FIG. 13B  provides one exemplary embodiment of a rotation-direction-limiting structure  1312  that is positioned in functional relation to each thrust paddle wheel  1311 . The exemplary rotation-direction-limiting structure  1312  comprises a ratchet mechanism. The ratchet mechanism includes a ratchet wheel  1306  rotationally connected to the SUP  1300  by a rotary bearing  1308  which is typically co-axial with the thrust paddle wheel rotary joint  1303 . The ratchet wheel  1306  comprises teeth  1307  that allow the ratchet wheel  1306  to rotate in the clockwise direction (in the figure) past the locking member  1309 , but not to rotate counter clockwise. The teeth  1307  may articulate to retract into the ratchet wheel  1306  when the ratchet wheel  1306  is rotating in the clockwise direction, or the locking member  1309  may comprise a cantilever spring that flexes upward in the figure to allow the teeth  1307  to pass under it when the ratchet wheel  1306  is rotating clockwise, but where the locking member  1309  does not buckle, but instead blocks the teeth  1307  from rotating past the locking member  1309  when the ratchet wheel  1306  is attempting to rotate in the counter-clockwise direction. 
     When the rider pushes the SUP  1300  rearward (i.e., to the left in the figure), the rotation-direction-limiting structure  1312  of  FIG. 13B  prevents counter-clockwise rotation of the thrust paddle wheels  1311 , which propels the SUP  1300  forward. Typically, two SUPs are used by a rider: one SUP for each foot of the rider, where each SUP is configured according to  FIGS. 13A and 13B , or functional equivalent. When the rider applies a forward thrust force to a first SUP, the thrust paddle wheels  1311  will not rotate, and thus the thrust paddles  1302  will not rotate, thereby applying a rearward force against the water. The second SUP that is gliding forward will have its thrust paddle wheels  1311  capable of rotating clockwise in the figure, and so the thrust paddles  1302  on its thrust paddle wheels  1311  will also rotate, and thereby not providing a material resistive force to forward motion. The rider then applies a forward thrust force to the second SUP while the first SUP is gliding forward. The result is that the rider may, in effect, skate on the surface of the water, using an alternating-foot sliding technique, similar to a Nordic snow skier. 
       FIG. 14A  is a top view of a solar-powered SUP  1400  in water  1401 . Sunshine provides solar energy that is stored by a battery  1413  and is also used to power a motor  1408  to propel the SUP  1400  in a desired direction at a desired speed. Solar cells  1402  are on the SUP  1400  visible to sunlight. The solar cells may be photovoltaic. The solar cells may comprise cadmium sulfide. The solar cells may be made of any convenient solar-power technology, and may be arranged in any convenient pattern. The solar cells  1402  communicate a control signal with the control circuitry  1404 , where the control signal may include control information to the solar cells  1402  and/or electrical power from the solar cells  1402 . The control signal may be communicated using electrical wires  1403 . The control circuitry  1402  communicates a battery signal with the battery  1413 . The battery signal may be communicated using electrical wires  1409  and  1410  to the battery terminals  1411  and  1412 , respectively. The control circuitry  1404  communicates a motor signal to a motor  1408 . The motor signal may be communicated using electrical wires  1407 , and the motor  1408  may be an electrical motor. The motor  1408  has an output shaft  1417  to which a pulley wheel  1414  is attached. Around the pulley wheel  1414  is a pulley belt  1416 . The pulley belt may pass by the side of the SUP  1400 ; however, shown in  FIG. 14A , the pulley belt  1416  may alternatively pass through an opening  1415  in the SUP  1400  to reach a mating pulley wheel. 
       FIG. 14B  is a side view of the solar-powered SUP  1400  of  FIG. 14A .  FIG. 14B  provides that the pulley belt  1416  passes through the opening  1415  and around a mating pulley wheel  1418 . The mating pulley wheel  1418  is capable of turning the pulley shaft  1419  that is supported by a bearing in the shaft support  1420  that is firmly affixed to the SUP  1400 . The pulley shaft  1419  is capable of turning the propeller shaft  1421  that turns the propeller  1422 . Any of a variety of convenient steering and breaking assemblies may be used with the SUP  1400 . In  FIG. 14B , a rear rudder  1424  is provided that is capable of rotating around a rudder shaft  1423 . 
     Speed and direction of the motor  1408  may also be controlled by a suitable controller. The controller may be wired or wireless. The controller may be a mobile device, such as an iPhone, iPad, Android mobile device, and the like. The controller may be hand held or mounted to the SUP  1400 . The controller may have buttons, rotary controls, squeeze controls, push controls, and the like. 
       FIG. 15A  is a side view of a useful embodiment of another thrust assembly. Such a thrust assembly may be substituted or combined with other thrust assemblies or actuators, such as the thrust actuators  902 ,  903 ,  904 ,  906 ,  907 , and  908 , of the SUPs  900  and  905  of  FIG. 9A , or the thrust assemblies of  FIGS. 10A-10D, 11A-11D, 12A-12D, and 13A-13B . In the thrust assembly of  FIG. 15A , the rider&#39;s foot  1502  is resting on the foot support  1503 . Alternately, a foot holder  1502  is removably secured to the foot support  1503 , and the rider&#39;s foot is held by the foot holder  1502 . The foot support  1503  may be attached to the SUP  1500  in a variety of ways. In  FIG. 15A , the foot support  1503  is supported relative to the surface of the SUP  1500  by a rotary joint  1504  connected to mount  1505  that is firmly affixed to the SUP  1500 . The SUP  1500  is floating in fluid  1501 , such as fresh or salt water. There is at least one thrust paddle  1509  with a rotary joint  1510  at one end capable of rotating relative to a mount  1511  which is firmly affixed to the SUP  1500 . In  FIG. 15A , there are additional thrust paddles  1515  and  1516 , with rotary joints  1513  and  1519 , respectively, and mounts  1514  and  1520 , respectively. A tie rod  1518  connects each of the thrust paddles  1509 ,  1515 , and  1516  by rotary joints  1508 ,  1512 , and  1517 , respectively. The foot support  1503  is also connected by a rotary joint  1506  to a connecting rod  1507  that is also connected to the rotary joint  1508 .  FIG. 15A  provides the rider&#39;s foot in a first position, and where the thrust paddles  1509 ,  1515 , and  1516  are in a retracted position, which produces very little resistance to water flow past the SUP  1500 . As shown in  FIG. 15B , when the rider presses down with the front part of their foot onto the foot support  1503 , the foot support  1503  rotates down, pushing on the connecting rod  1507 , and causing the thrust paddles  1509 ,  1515 , and  1516  to rotate counter clockwise to an extended position, extending downward deeper into the water. In the extended position, a thrust paddle is capable of applying a force against the water supporting the SUP  1500 . Note that rotating the front part of the foot support  1503  down places the rider&#39;s foot and leg in a convenient orientation to press rearward. Typically, two SUPs are used by a rider: one SUP for each foot of the rider, where each SUP is configured according to  FIG. 15A . When the rider shifts their weight from the front of the foot on a first SUP that is pressing rearward, to the front of the foot on the second SUP that is gliding forward, the thrust paddles of the second SUP will be rotate into the extended position capable of applying a rearward force against the water. When the rider applies a rearward force with the second SUP, the first SUP that is not supporting the rider&#39;s weight will have thrust paddles in the retracted position provided by  FIG. 15B , and will not provide a resistive force to forward gliding motion. The result is that the rider may, in effect, skate on the surface of the water, using a weight-shifting sliding technique similar to a Nordic snow skier. 
       FIG. 16  is a top view of an exemplary apparatus that prevents a plurality of SUPs from coming into contact with each other, and allows the SUPs to move uninhibited in a substantially parallel direction relative to each other along a desired direction of travel. Such an apparatus, or functionally equivalent thereto, finds particular use when a rider uses a dual-SUP apparatus, including but not limited to one of the apparatuses provided by  FIGS. 9A, 10A-10D, 11A-11D, 12A-12D, and 13A-13B  to, in effect, skate on the surface of the water, using a dual-SUP sliding technique similar to a Nordic snow skier. This list of figures above is intended only to exemplify use cases for the apparatus of  FIG. 16 , and the list is not intended to be complete or to limit the use cases. When the rider slides each foot forward and rearward, the exemplary apparatus comprises limit-stop structures that limit the rotation of articulated links between the two SUPs in order to prevent one SUP from undesirably contacting the other SUP. The exemplary apparatus of  FIG. 16  permits two SUPs to slide freely parallel to each other, and the two SUPs may move toward and away from each other, but only in distance amounts limited by the placement of the limit-stop structures. Wheels along the sides between the two SUPs, as well as protective bumpers along the sides and between the two SUPs may also be used. 
     SUP  1600  is an SUP supporting a left foot  1603  of a rider on water  1601 . Similarly, SUP  1602  is an SUP supporting a right foot  1604  of the rider on water  1601 . A first articulated linkage comprises a left link  1606  with a left rotary joint  1605  connected to a left mount  1615  that is affixed to the left SUP  1600 . The left link  1606  also has a right rotary joint  1607  connected to a floating mount  1608  that is not affixed to an SUP. The first articulated linkage comprises a right link  1610  with a left rotary joint  1609  connected to the floating mount  1608 . The right link  1610  also has a right rotary joint  1611  connected to a right mount  1612  that is affixed to the right SUP  1602 . Each of the mounts  1615 ,  1608 , and  1612  comprises a limit-stop structure to prevent each link from rotating past a desired point. The limit-stop structures may comprise a pin, protrusion, or other convenient structure to prevent rotation of a rotating member beyond a desired angle. The left link  1606  is prevented from rotating in the counter-clockwise direction relative to the left mount  1615  by a limit-stop structure  1614 . Similarly, the left link  1606  is prevented from rotating in the clockwise direction relative to the left mount  1615  by a limit-stop structure  1613 . The left link  1606  is prevented from rotating in the counter-clockwise direction relative to the floating mount  1608  by a limit-stop structure  1616 . The right link  1610  is prevented from rotating in the counter-clockwise direction relative to the right mount  1612  by a limit-stop structure  1618 . Similarly, the right link  1610  is prevented from rotating in the clockwise direction relative to the right mount  1612  by a limit-stop structure  1619 . The right link  1610  is prevented from rotating in the clockwise direction relative to the floating mount  1608  by a limit-stop structure  1617 . 
     An optional second articulated linkage comprises a left link  1622  with a left rotary joint  1621  connected to a left mount  1620  that is affixed to the left SUP  1600 . The left link  1622  also has a right rotary joint  1623  connected to a floating mount  1624  that is not affixed to an SUP. The optional second articulated linkage comprises a right link  1626  with a left rotary joint  1625  connected to the floating mount  1624 . The right link  1626  also has a right rotary joint  1627  connected to a right mount  1628  that is affixed to the right SUP  1602 . Each of the mounts  1620 ,  1624 , and  1628  comprises a limit-stop structure to prevent each link from rotating past a desired point. The limit-stop structures may comprise a pin, protrusion, or other convenient structure to prevent rotation of a rotating member beyond a desired angle. The left link  1620  is prevented from rotating in the counter-clockwise direction relative to the left mount  1620  by a limit-stop structure  1631 . Similarly, the left link  1622  is prevented from rotating in the clockwise direction relative to the left mount  1620  by a limit-stop structure  1632 . The left link  1622  is prevented from rotating in the counter-clockwise direction relative to the floating mount  1624  by a limit-stop structure  1633 . The right link  1626  is prevented from rotating in the counter-clockwise direction relative to the right mount  1628  by a limit-stop structure  1630 . Similarly, the right link  1626  is prevented from rotating in the clockwise direction relative to the right mount  1628  by a limit-stop structure  1629 . The right link  1626  is prevented from rotating in the clockwise direction relative to the floating mount  1624  by a limit-stop structure  1634 . 
       FIG. 17  is a top view of an exemplary apparatus that protects a plurality of SUPs when they contact each other. Such an apparatus, or functionally equivalent thereto, finds particular use when a rider uses a dual-SUP apparatus, including but not limited to one of the apparatuses provided by  FIGS. 9A, 10A-10D, 11A-11D, 12A-12D, and 13A-13B  to, in effect, skate on the surface of the water, using a dual-SUP sliding technique similar to a Nordic snow skier. This list of figures above is intended only to exemplify use cases for the apparatus of  FIG. 17 , and the list is not intended to be complete or to limit the use cases. 
     In  FIG. 17 , wheels may be placed along the sides of the two SUPs  1700  and  1701  and between the two SUPs  1700  and  1701 . Protective bumpers may also be placed along the sides of and between the two SUPs  1700  and  1701 . SUP  1700  is an SUP supporting a left foot  1703  of a rider on water  1702 . Similarly, SUP  1701  is an SUP supporting a right foot  1704  of the rider on water  1702 . In this exemplary embodiment, the left SUP  1700  comprises a plurality of wheels on side facing the right SUP  1701 . One or more wheels  1705  rotate around a rotary joint  1706  that is supported by a mount  1707  that is affixed to the SUP  1700 . In  FIG. 17 , a front and rear wheel assembly are provided, although, any number of wheel assemblies may be used. A protective bumper  1708  is attached to the right SUP  1701 ; however, either SUP may comprise one or more wheel assemblies, and either SUP may comprise a protective bumper, or either SUP may comprise both one or more wheel assemblies as well as a bumper. The protective bumper  1708  may help prevent one SUP from damaging the other SUP if they come into contact, whether or not wheels  1705  are included. The protective bumper  1708  may also provide a useful surface to roll against by one or more wheels  1705  located on the side of the other SUP. 
       FIG. 18A  is a prospective view of a floatation apparatus. A foot holder  1800  is capable of receiving a foot  1803 . The foot may be inserted in the direction of the arrow  1804  into a cavity  1802  in the foot holder  1800 . The foot holder  1800  is capable of floating on the water  1801 . The foot holder  1800  may have a density below the density of water so a wearer will not fully submerge into the water  1801  when wearing one or more foot holders  1800 . The foot holder  1800  may comprise low-density foam. The foot holder  1800  may be inflated with fluid with a density lower than water, where such fluid may comprise air or another gas, including but not limited to helium. When the foot holder  1800  is inflated, the foot holder  1800  may be made of plastic, vinyl, Mylar, or any other convenient material capable of containing a gas. The type of plastic commonly used to manufacture kayaks may be used. The foot holder  1800  may be made from plastic and coated on the inside or outside with sealant further to reduce its permeability to a gas it&#39;s intended to contain, such as helium. The size of the foot holder  1800 , the gas and pressure it is inflated with, as well as the weight of the wearer, determine whether the wearer will float or sink while wearing one or more foot holders  1800 . The wearer may use balancing poles similar to those found in  FIG. 9A , such as extension  931  with handle  930  and floating member  932 . When a foot holder  1800  is worn on each foot, the result is that the wearer may, in effect, walk on the surface of the water. 
       FIG. 18B  is a perspective view of a foot holder  1807 . The foot holder  1807  may be removably secured to the floatation member  1805 . The foot holder  1807  is capable of receiving a foot  1809 . The foot may be inserted in the direction of the arrow  1810  into a cavity  1808  in the foot holder  1807 . The floatation member  1805  may be an SUP, typically a smaller-than-usual SUP, typically one small SUP for each foot of wearer, where the small SUP includes but is not limited to a smaller-than-usual version of a stand-up paddle board, surf board, kayak, canoe, pontoon, or any of a variety of buoyant objects, boards, boats, inflatable devices, and the like, or any other functionally similar floatation or buoyant apparatus, where the apparatus may comprise a plurality of floatation or buoyant members, and where the apparatus is capable of providing buoyancy support for at least one user or rider in a fluid, which may be water. The floatation member  1805  may comprise low-density foam. The floatation member  1805  may be inflated with fluid with a density lower than water, where such fluid may comprise air or another gas, including but not limited to helium. When the floatation member  1805  is inflated, the floatation member  1805  may be made of plastic, vinyl, Mylar, or any other convenient material capable of containing a gas. The type of plastic commonly used to manufacture kayaks may be used. The floatation member  1805  may be made from plastic and coated on the inside or outside with sealant further to reduce its permeability to a gas it&#39;s intended to contain, such as helium. When a foot holder  1807  with floatation member  1805  is worn on each foot, the result is that the wearer may, in effect, walk on the surface of the water. 
       FIG. 19A  is a side view of a useful embodiment of another thrust assembly. Such a thrust assembly may be substituted or combined with other thrust assemblies or actuators, such as the thrust actuators  902 ,  903 ,  904 ,  906 ,  907 , and  908 , of the SUPs  900  and  905  of  FIG. 9A , or the thrust assemblies of  FIGS. 10A-10D, 11A-11D, 12A-12D, 13A-13B , and  15 A- 15 B. In the thrust assembly of  FIG. 19A , the rider&#39;s foot is resting on the foot support  1903 . Alternately, a foot holder  1902  is removably secured to the foot support  1903 , and the rider&#39;s foot is held by the foot holder  1902 . The foot support  1903  may be attached to the SUP  1900  in a variety of ways. The SUP  1900  is floating in fluid  1901 , such as fresh or salt water. There is at least one thrust paddle wheel  1918  capable of rotating about a rotary joint  1917  relative to the SUP  1900 . There are a plurality of thrust paddles  1919  affixed to each thrust paddle wheel  1918 , where the number of thrust paddles  1919  per thrust paddle wheel  1918  is typically at least four so that at least one thrust paddle  1919  will be in the water at all times. 
     Similar to a bicycle ratchet hub, each thrust paddle wheel may comprise a rotation-direction-limiting structure capable of preventing the associated thrust paddle wheel  1918  from rotating counter clockwise in the figure relative to the crank arm  1916  during a forward-thrust phase, but allows each thrust paddle wheel  1918  to rotate clockwise in the figure relative to the crank arm  1916  with little resistance when the crank arm  1916  is stationary, or rotating slowly. 
     The foot support  1903  is connected to the push rod  1914  by a rotary joint  1907 . The rotary joint  1907  may also comprise a wheel  1906  on which the foot support  1903  may roll relative to the SUP  1900 . The push rod  1914  is connected to the crank arm  1916  by a rotary joint  1915 . When the crank arm  1916  is rotated clockwise, it causes the thrust paddle wheel  1918  to rotate clockwise. If the thrust paddle wheel  1918  comprises a hub that functions similarly to a bicycle ratchet hub, the thrust paddle wheel  1918  will prevent the crank arm  1916  from rotating counter clockwise. The foot support  1903  is also connected to the tie rod  1908  by a rotary joint  1905 . The rotary joint  1905  may also comprise a wheel  1904  on which the foot support  1903  may roll relative to the SUP  1900 . The tie rod  1908  is connected to a hand lever  1910  by a rotary joint  1909 . With the rotary joint  1911 , the hand lever  1910  can rotate relative to the lever mount  1912  which is affixed to the SUP  1900 . Accordingly, when the rider pushes the foot support  1903  forward (i.e., to the right in the figure), the foot support  1903  pulls the connecting rod  1914  to the right, which causes the crank arm  1916  to rotate clockwise in the figure, causing the thrust paddle wheel  1918  also to rotate clockwise, which propels the SUP  1900  forward. Sliding the foot support  1903  forward may be aided by simultaneously pulling rearward (i.e., to the left in the figure) of the handle  1913 . Pulling rearward of the handle  1913  causes the hand lever  1910  to rotate counter clockwise, thus pulling on the tie rod  1908 , which assists in pulling the foot support  1903  to the right. The SUP  1900  may comprise a fender  1920  to prevent water from splashing from the paddle wheel  1918  onto the SUP  1900  or the rider. 
       FIG. 19B  is a plan view of two SUPs according to  FIG. 19A . Although the two SUPs  1921  and  1900  are provided in  FIG. 19B  linked together, they need not be connected. One SUP according to  FIG. 19A  may be used alone; however, typically, two SUPs are used by a rider: one SUP for each foot of the rider, where each SUP is configured according to  FIG. 19A , or functional equivalent. In  FIG. 19B , for clarity of the drawing, although the SUP  1921  includes all of the apparatus that is shown for the SUP  1900 , the SUP  1921  does not show all of the apparatus that is shown for the SUP  1900 . According to  FIG. 19B , when the rider applies a forward thrust force to the foot support  1903  of SUP  1900 , the thrust paddle wheel will rotate, and so the thrust paddles  1919  will rotate, thereby applying a force against the water causing the SUP  1900  to move forward (i.e., to the right in the figure). If the rider doesn&#39;t apply a forward thrust force to the foot support of SUP  1921 , but SUP  1921  comprises a hub that functions similarly to a bicycle ratchet hub, the SUP  1921  will glide forward with its thrust paddles rotating clockwise in the figure due to water  1901  flowing by the moving SUP  1921 , and so while gliding, the thrust paddles of SUP  1921  do not provide a material resistive force to forward motion. The rider then applies a forward thrust force to the SUP  1921  while the SUP  1900  is gliding forward. The result is that the rider may, in effect, skate on the surface of the water, using an alternating-foot sliding technique, similar to a Nordic snow skier. 
       FIG. 19C  is a rear-end view of the SUPs shown as connected in  FIG. 19B . The connection allows for one SUP to pull the other SUP in the forward direction, but also allows each SUP to rotate about an axis  1957  relative to the other SUP. The dashed line  1961  shows the outline of the SUP  1900  rotated clockwise, and the dashed line  1960  shows the outline of the SUP  1921  rotated counter clockwise. Such rotations may occur as water waves pass beneath each SUP at different times. The rider may also intentionally rotate an SUP to aid in steering. The rotations may include limit-stop apparatus to prevent the angle between the two SUPs from exceeding a maximum angle. The rider may decide to prevent the two SUPs from rotating relative to each other, and modify the articulated connections between the two SUPs to prevent or limit the rotation. 
       FIG. 19B  comprises a forward connection joint with a left link  1948  connected to a right link  1949  by a rotary joint with an axis  1952 . The axis  1952  is shown to be substantially in line with the forward direction of travel of the two SUPs. A pin may be used to connect the right link  1949  with the left link  1948 , where the pin has a forward end  1950  and a rearward end  1951 . The non-pinned end of the right link  1949  is affixed to the right SUP  1900 , and the non-pinned end of the left link  1948  is affixed to the left SUP  1921 . 
       FIG. 19B  also comprises an optional rear connection joint with a left link  1953  connected to a right link  1954  by a rotary joint with an axis  1957 . The axis  1957  is shown to be substantially in line with the forward direction of travel of the two SUPs, and also co-linear with the axis  1952 . A pin may be used to connect the right link  1954  with the left link  1953 , where the pin has a forward end  1955  and a rearward end  1956 . The non-pinned end of the right link  1954  is affixed to the right SUP  1900 , and the non-pinned end of the left link  1953  is affixed to the left SUP  1921 . 
     Additional numbered elements of  FIG. 19B  include front  1928  and rear  1927  axils for the right-side front  1904  and rear  1906  wheels, respectively, of the right foot support  1903 . The right foot support  1903  may comprise left-side front and rear wheels  1947 . The right foot support  1903  is connected by the connector  1930  to the tie rod  1908 , and connected by the connector  1940  to the push rod  1914 . The hand lever  1910  is connected by the connector  1937  to the lever mount  1912 , where the connector  1937  has a left end  1938 . The crank arm  1916  is connected to the paddle wheel  1918  by a connector  1945 . The SUP  1921  may comprise a fender  1958  to prevent water from splashing from the paddle wheel thrust paddles  1959  onto the SUP  1921  or the rider. 
       FIG. 19D  is a side view of a useful embodiment of another thrust assembly. This thrust assembly comprises an elliptical-exercise-bike-style thrust assembly attached to a paddle wheel. When a paddle wheel is used, a water splash guard, such as a fender, may be used. The thrust assembly may also be mechanically connected to a propeller or other thrust actuator. The thrust assembly allows the rider of the SUP to use one or both arms, one or both legs, or any combination thereof to generate thrust. Steering and braking may comprise wired or wireless controls and actuators. 
     The elliptical-exercise-bike-style mechanism may be used on one or a pair of flotation devices. When a pair of floatation devices are used, they may be functionally connected. The floatation devices may be capable of rotating relative to each other. The floatation devices may be inflated. They may be filled will low-density fluid, such as a gas. 
     In  FIG. 19D , the handle  1979  is connected to the hand lever  1977  which pivots relative to the lever mount  1983  that is attached to the SUP  1962  floating on the water  1963 . A foot holder  1964  may be attached to a foot support  1965  on the end of a foot lever  1966  that is connected to the hand lever  1977  by a revolute joint  1976 . The paddle wheel  1972  has paddle blades  1973 , and the paddle wheel rotates about a rotary axis  1975  on a paddle-wheel mount  1974 . The paddle wheel  1972  is connected by a revolute joint  1971  to a connecting rod  1968  that also connects to the foot lever  1966  by a revolute joint  1967 . The connecting rod  1968  rolls relative to the SUP  1962  by a wheel  1969  with an axis  1970 . A rudder  1981  may rotate about an axis  1982  to steer the SUP  1962 . 
       FIG. 20A  is a side view of a useful embodiment of another thrust assembly. The thrust assembly allows the rider of the SUP  2000  to use one or both arms, one or both legs, or any combination thereof to generate thrust. Shown is a thrust assembly for use by a right arm and leg. A foot may rest on the foot support  2003 , or a foot holder  2002  may be attached to the foot support  2003 . The foot holder  2002  may comprise a water sock or waterski boot. Steering and braking may comprise wired or wireless controls and actuators. When the rider pulls rearward on the handle  2029  of the hand lever  2027 , the hand lever  2027  rotates about a revolute joint  2028  on a lever support  2030  connected to the SUP  2000 . The hand lever  2027  then pulls the connecting rod  2025  that is connected to the hand lever  2027  by the revolute joint  2026 . The connecting rod  2025  pulls the lever arm  2023  by the revolute joint  2024 , which causes the thrust paddles  2015 ,  2014 , and  2013  to rotate clockwise to a non-activated position, allowing the foot carriage  2007 , to which the thrust paddles  2015 ,  2014 , and  2013  are rotationally attached, to slide forward with only minimal water resistance. The thrust paddles  2015 ,  2014 , and  2013  rotate relative to the carriage  2007  about the revolute joints  2022 ,  2021 , and  2020 , respectively. The lever arm  2023  is connected to the thrust paddle  2015 , which when the lever arm  2023  is rotated, it rotates the thrust paddles  2015 ,  2014 , and  2013  by the connecting rod  2019  pinned to each thrust paddle  2015 ,  2014 , and  2013  by the revolute joints  2018 ,  2017 , and  2016 , respectively. Pulling rearward on the handle  2029  additionally assists in moving the foot carriage  2007  forward. Pushing forward on the handle  2029  causes the thrust paddles  2015 ,  2014 , and  2013  to rotate counter clockwise, and assists in moving the foot carriage  2007  rearward to propel the SUP  2000  forward in the water  2001 . The foot support  2003  may be rotatably connected to the foot carriage  2007 , making it easier and more comfortable for the rider to lift their heel during a thrust phase where the rider pushes their foot rearward. As shown, a foot-supported hinge  2004  is connected to a carriage hinge  2006  by a hinge joint  2005 . A rotational support structure  2008  acts as a limit stop and prevents the foot support  2003  from rotating counter clockwise too far. In  FIG. 20A , the foot carriage  2007  may comprise one or more wheels  2009  and  2010  that rotate about axes  2011  and  2012 , respectively, to move relative to the SUP  2000 . There are limit stops on the front  2031  and rear  2032  of the SUP  2000  to prevent the foot carriage  2007  from moving too far forward or rearward. Steering and braking may use any convenient means. A rudder  2034  may rotate about an axis  2033  to steer the SUP  2000 . The hand lever may be substituted by handle bars. Thrust paddles limit-stop structure may be added, such as to the foot carriage  2007 , to prevent the thrust paddles  2015 ,  2014 , and  2013  from rotating beyond a desired point. 
       FIG. 20B  is a side view of a useful embodiment of another thrust assembly.  FIG. 20B  is similar in structure to  FIG. 20A  with corresponding elements and element numbering, except the foot carriage includes a linear bearing  2037 , which may be in addition to, or in place of, the wheels  2009  and  2010  of  FIG. 20A . The linear bearing  2037  is guided by the bearing shaft  2036  (with length that is not drawn to scale) with front  2035  and rear  2039  shaft supports connected to the SUP  2000 . The rotational support structure that acts as a limit stop  2038  is shown to be longer to reach to the SUP  2000  in  FIG. 20B ; whereas the rotational support structure  2008  of  FIG. 20A  is shown shorter to rest on the foot carriage  2007 . 
       FIG. 20C  is a rear-end view of the thrust assembly of  FIG. 20B , with corresponding elements and element numbering, and with some additional elements numbered that are visible in  FIG. 20C . For clarity of  FIG. 20C , the rotational support structure  2038  in  FIG. 20B  that prevents the foot support from rotating counter clockwise too far, is not shown in  FIG. 20C . The connecting rod  2019  is connected to the thrust paddle  2013  by a connector  2039  with an end  2040 . The thrust paddle  2013  is connected to the linear bearing  2037  by a connector  2047 . The foot support  2003  further comprises a left linear bearing  2041  and left bearing shaft  2042  with the left shaft support  2043  connected to the SUP  2000 . A left foot-supported hinge  2046  is connected to a left carriage hinge  2044  by a left hinge joint  2045 . 
       FIG. 21A  is a plan view of a useful embodiment of another thrust assembly. The SUP  2100  has one or a plurality of treadmill belts.  FIG. 21A  provides a right  2109  and left  2108  treadmill belt. As the rider walks or runs on the treadmill belts, thrust paddles (not shown in this view) in contact with the water  2101  apply force against the water  2101  to move the SUP  2100  forward. The rider places their right foot on the right treadmill belt  2109 . The right treadmill belt  2109  may comprise a right foot holder  2110 , similar to  FIGS. 9E and 9F , connected to a right holder base  2111 , typically at the toe end  2112 . Alternately, the toe end  2112  may be hinged to the surface of the right treadmill belt  2109 . The left treadmill belt  2108  may comprise a left foot holder  2105 , similar to  FIGS. 9E and 9F , connected to a left holder base  2106 , typically at the toe end  2107 . Alternately, the toe end  2107  may be hinged to the surface of the left treadmill belt  2108 . The SUP  2100  may comprise a handlebar  2102  for steering, with handle  2103  and shaft  2104 . 
       FIG. 21B  is a side view of the thrust assembly of  FIG. 21A . Similar to the foot holder  945  of  FIGS. 9E and 9F , here the holder base  2111  is shown to comprise loop Velcro  2113  attached to hook Velcro  2114 , which is attached to the treadmill belt  2109 . The thrust paddles  2128 ,  2129 ,  2130 , and  2131  may comprise rotation limit stops  2131 ,  2127 ,  2122 , and  2123 , such that the thrust paddles  2128  and  2129  are in an active extended position when applying force to the water, and the thrust paddles  2130  and  2131  are in an inactive retracted position when in a recovery phase. The thrust paddles  2128 ,  2129 ,  2130 , and  2131  may collapse to the retracted position to permit gliding. The thrust paddles  2128 ,  2129 ,  2130 , and  2131  may move with a circulatory belt  2115 , as shown in  FIG. 21B . Various mechanical or electrical means may be used to connect the treadmill belt control input to moving the thrust paddles  2128 ,  2129 ,  2130 , and  2131 . In  FIG. 21B , the control treadmill  2109  uses pulley wheels  2116  and  2121  and figure-8 belts  2120  and  2125 , respectively, to transfer rider-generated motion to the pulley wheels  2118  and  2123 , respectively, of the circulatory belt  2115  moving the thrust paddles  2128 ,  2129 ,  2130 , and  2131 . The thrust paddles  2128 ,  2129 ,  2130 , and  2131  rotate about axes  2132 ,  2135 ,  2138 , and  2141 , respectively, relative to the bases  2133 ,  2136 ,  2139 , and  2142 , respectively attached to the circulatory belt  2115 . The pulleys  2116 ,  2121 ,  2118 , and  2123  have rotary axes  2117 ,  2122 ,  2119 , and  2124 , respectively. The entire thrust assembly may reside in a cavity of the SUP  2100 , with a front cavity boundary  2126  and a rear cavity boundary  2127 . The handle  2103  of the handlebars may steer the direction of the rudder  2175 . There is typically at least one thrust paddle  2128 ,  2129 ,  2130 , and  2131  in the water  2101  on the bottom side of the circulatory belt  2115 . 
       FIG. 21C  is a side view, where the thrust paddles on the circulatory belt  2115  in  FIG. 21B  are substituted with collapsible thrust actuators or “scoop fins”  2155 ,  2158 ,  2152 , and  2149  on the circulatory belt  2144  in  FIG. 21C , such as were introduced in  FIGS. 9A-9D . The two top thrust actuators  2155  and  2158  are shown with their respective ends  2156  and  2159  collapsed; whereas, the two bottom thrust actuators  2152  and  2149  are shown with their respective ends  2153  and  2150  open and capable of catching water to apply thrust. The thrust actuators  2155 ,  2158 ,  2152 , and  2149  comprise sides  2157 ,  2160 ,  2154 , and  2151 , respectively. The circulatory belt  2144  comprises belt rollers  2145  and  2147  with axes  2146  and  2148 , respectively. 
       FIG. 21D  is a side view, where the pulleys and belt of  FIG. 21A  that mechanically connect[[s]] the treadmill  2161  control input with the circulatory belt  2164  output is replaced by fixed gears  2162  and  2163  providing rearward transmission from the top treadmill  2161  to rearward transmission of the bottom circulatory belt  2164 . The top gear  2162  may be a 1-way ratchet gear, like a bicycle sprocket or functional equivalent, where when the top treadmill  2161  is recovered forward, the top gear  2162  does not drive the bottom circulatory belt  2164  forward. A ratchet gear on the bottom gear  2163  allows fixed thrust actuators that don&#39;t rotate relative to the circulatory belt  2164  during gliding. Although not explicitly shown in  FIG. 21D , the top treadmill  2161  is typically where the rider stands, and the top treadmill  2161  may comprise a foot holder similar to the foot holder  2110  in  FIG. 21B . 
       FIG. 21E  is an end view, where the fixed gears  2161  and  2163  of  FIG. 21D  are replaced by a gear box, which may also comprise an apparatus to provide a continuously changeable gear ratio. For example, the top gears  2166 ,  2162 , and  2169  are coaxial with the top treadmill  2161  and can each rotate the top treadmill  2161 . The axil  2165  of the top treadmill  2161  is attached to the gear  2166  having the axil  2167 , which is attached to the gear  2162  having the axil  2168 , which is attached to the gear  2169 . The bottom gears  2171 ,  2163 , and  2174  are coaxial with the bottom circulatory belt  2164  and can each rotate the bottom circulatory belt  2164 . The axil of the bottom circulatory belt  2164  is capable of sliding to extend, where one of the sliding ends  2170  is attached to the gear  2171  having the axil  2172 , which is attached to the gear  2163  having the axil  2173 , which is attached to the gear  2174 . As shown, the first gear  2166  of the top treadmill  2161  is meshed with the first gear  2171  of the bottom circulatory belt  2164 , providing a first gear ratio. When the sliding axil of the bottom circulatory belt  2164  is extended by the rider, the second gear  2162  of the top treadmill  2161  is meshed with the second gear  2163  of the bottom circulatory belt  2164 , providing a second gear ratio. When the sliding axil of the bottom circulatory belt  2164  is further extended, the third gear  2169  of the top treadmill  2161  is meshed with the third gear  2174  of the bottom circulatory belt  2164 , providing a third gear ratio. 
       FIG. 22A  is a rear-end view of the thrust assembly of  FIG. 22B , where  FIG. 22B  is a side view of a useful embodiment of another thrust assembly. Right  2206  and left  2223  foot carriages roll on wheels  2208 ,  2212 ,  2225 , and  2230  along linear rails  2210 ,  2213 ,  2227 , and  2231  having rail bases  2209  and  2226 , much like freight train wheels roll along railroad tracks. The wheels  2208 ,  2212 ,  2225 , and  2230  may have larger-diameter disks on either the inside surface of the wheels  2208 ,  2212 ,  2225 , and  2230 , the outside surface of the wheels, or both. In  FIG. 22A , the wheels  2208 ,  2212 ,  2225 , and  2230  are shown with larger-diameter disks on both the inside and outside surfaces of the wheels to better guide the food carriages  2206  and  2223  along the linear rails  2210 ,  2213 ,  2227 , and  2231 .  FIG. 22A  provides optional upper rails  2211 ,  2214 ,  2228 , and  2232  to prevent the foot carriages  2206  and  2223  from coming off the lower rails  2210 ,  2213 ,  2227 , and  2231 . Thrust paddles  2219  and  2235  extend from the foot carriages  2206  and  2223  through openings, such as slots, along the SUP  2247 , with sections  2202 ,  2238 ,  2200 ,  2239 , and  2203 . The thrust paddles  2219  and  2235  may rotate relative to the foot carriages  2206  and  2223 , and the rotation may be impeded by limit stops  2243  and  2246  in  FIG. 22B  for the thrust paddles  2219  and  2244 , respectively. The limit stops  2243  and  2246  in  FIG. 22B  are useful to help the thrust paddles  2219  and  2235  apply a forward thrust force to propel the SUP  2247 , but where the thrust paddles  2219  and  2235  may rotate clockwise so as not to provide drag during a recovery phase. In this way, the thrust paddles  2219  and  2235  may be used to apply force against the water  2201  to propel the SUP  2247  forward (i.e., to the right in  FIG. 22B ). The thrust paddles  2219  and  2235  may be linked together by a tie rod (not shown), similar to the tie rod  1518  in  FIGS. 15A-15B . 
     The rider typically places their feet on the carriages  2206  and  2223 . The carriages  2206  and  2223  may comprise foot holders  2204  and  2221  with foot supports  2205  and  2222 , respectively. The carriages  2206  and  2223  connect to the wheels  2208 ,  2212 ,  2225 , and  2230  by axils  2207 ,  2215 ,  2224 , and  2229 , respectively. The axils of the wheels  2208 ,  2212 ,  2225 , and  2230  connect to the paddle supports  2216 ,  2217 ,  2233 , and  2236 . The paddle supports  2216 ,  2217 ,  2233 , and  2236  connect to paddles  2219  and  2235  by revolute joints  2218 ,  2220 ,  2234 , and  2237 . 
       FIG. 22B  provides a front right thrust paddle  2244  with revolute joint  2245  and limit stop  2246 , as well as a front right wheel  2241  with an axil  2242 . The foot holder  2204  may comprise Velcro  2240  to attach to the carriage  2206 . The upper  2211  and lower  2210  rails may comprise front  2248  and rear  2249  rail supports attached to the SUP  2247 . 
       FIGS. 23A-23D  provide a wireless steering apparatus.  FIG. 23A  is a side view of a wireless steering control apparatus comprising a foot holder  2301  connected to a foot support  2302  comprising a first mating portion  2303  mated with a second mating portion  2304 . The foot support  2302  may comprise hard, flexible rubber. The second mating portion  2304  is connected to a rotary member  2305  with a rotary joint  2306  for rotating relative to a base  2300 . The base may be affixed to an SUP, or the base may be the SUP itself. The base  2300  may be functionally equivalent to the support member  2206  of the foot carriage in  FIG. 22A . 
       FIG. 23B  is a plan view of the wireless steering control apparatus of  FIG. 23A  in a straight orientation. 
       FIG. 23C  is a plan view of the wireless steering apparatus of  FIG. 23A  in a left-turn orientation. Rotary joint  2306  comprises an angular sensor and wirelessly transmits an angle signal to a wireless steering actuator. 
       FIG. 23D  is a side cutaway view of a wireless steering actuator. Located inside a water-resistant container  2307  is control circuitry  2308 , a battery  2310 , a rotation actuator  2312 , transmission apparatus  2314  and  2315 , and related electrical and mechanical connections. The transmission apparatus is connected to a steering rudder  2317 . The control circuitry  2308  comprises a wireless receiver for receiving a wireless angle signal, and optionally a wireless transmitter. The control circuitry  2308  typically comprises a digital processor for processing data. The control circuitry  2308  may be connected by wires  2309  to the battery  2310 . The control circuitry  2308  may also be connected by wires  2311  to the rotation actuator  2312 . The rotation actuator  2312  may be an electric motor with an output shaft  2313 . The output shaft  2313  may be connected to an input gear  2314  which meshes with, or is connected by a belt or cable to, an output gear  2315 . The output gear  2315  is connected to the rudder shaft  2316  which controls the orientation of the rudder  2317 . Accordingly, the rider of the SUP  2318  may control the rudder  2317  by rotating their foot. Alternatively, the rider or someone else may use a mobile communication device, such as a tablet or phone, to control the rudder  2317 . 
       FIG. 24A  is a perspective view of a thrust paddle  2400  with a curved paddle edge  2402 . The thrust paddle  2400  may have a rotary joint  2401  about which it rotates. The thrust paddle  2400  typically has a straight edge  2403  on the edge nearest the rotary joint  2401 . The curved paddle edge  2402  is typically the paddle edge most distal from the rotary joint  2401 . The curved paddle edge  2402  is helpful to catch water when the thrust paddle  2400  is in a retracted orientation, and when the thrust paddle  2400  is moved in the direction from the straight edge  2403  toward the curved paddle edge  2402 . When the thrust paddle  2400  is translated in this direction, the curved paddle edge  2402  acts like a scoop, and water fills a cavity formed by the curved paddle edge  2402 , where the water applies a force against the thrust paddle  2400  and rotates the curved paddle edge  2402  downward into deeper water into a thrust-capable orientation. 
       FIG. 24B  is a cross section  2404  of the thrust paddle  2400  near the curved paddle edge  2402 . 
       FIG. 24C  is a cross section  2405  of the thrust paddle  2400  midway between the curved paddle edge  2402  and the straight edge  2403 . 
       FIG. 24D  is a cross section  2406  of the thrust paddle  2400  near the straight edge  2403 . 
       FIG. 25A  is a rear-end view of the thrust assembly of  FIG. 25B , where  FIG. 25B  is a side view of a useful embodiment of another thrust assembly. A right-foot carriage  2506  rolls on wheels  2509  and  2519  along rolling surfaces  2515  and  2524 . The wheels  2509  and  2519  may comprise rubber, and the rolling surfaces  2515  and  2524  may comprise strips of metal. Typically there is a similar left-foot carriage, but for clarity, it is not shown in  FIGS. 25A-25B .  FIG. 25A  provides a linear bearing  2516  with bearing rail  2517  to guide the foot carriage  2506 . A thrust paddle  2414  extends from the foot carriage  2506  through openings, such as slots, along the SUP  2500  having additional sections  2501  and  2502 . The SUP  2500  may comprise a handlebar for turning a rudder, such as provided by  FIG. 21B . The thrust paddle  2514  may rotate relative to the foot carriage  2506 , and the rotation of the thrust paddle  2514  may be impeded by limit stops. In  FIG. 25B , thrust paddles  2514  and  2529  have limit stops  2528  and  2532 , respectively. In this way, the thrust paddles  2514  and  2529  may be used to apply force against the water  2503  to propel the SUP  2500  forward (i.e., to the right in  FIG. 25B ). The limit stops  2528  and  2512  may be adjustable to vary the depth the thrust paddles  2514  and  2529  (which may also be called “louvres”) will extend, which accordingly varies the amount of effort the rider must exert based on the amount of water “grip.” The limit stops  2528  and  2512  may be adjusted by a control in a handle, a grip, or handlebar (not shown), and where a Bowden cable may be used. One or more thrust paddles, such as thrust paddles  2514  and  2529 , may be linked together by a tie rod  2527  by revolute joints  2526  and  2530 , respectively. As the rider slides their feet alternately forward and rearward, similar to a Nordic snow skier, thrust paddles in contact with the water  2503  apply force against the water  2503  to move the SUP  2500  forward. 
     The rider typically places their feet on the carriage  2506 . The carriage  2506  may comprise a foot holder  2504  with a foot support  2505 . The foot holder  2504  may comprise a water sock or a boot. The carriage  2506  connects to the wheels  2509  and  2519  by axils  2508  and  2518 , respectively. The axils  2510  and  2520  of the wheels  2509  and  2519  connect to the paddle supports  2511  and  2521 , and may be seen from the sides as axils  2512  and  2522 , respectively. The paddle supports  2511  and  2521  connect to the paddle  2514  by revolute joints  2513  and  2523 . 
       FIG. 25B  provides a front right thrust paddle  2529  with revolute joint  2531  and limit stop  2532 , as well as a front right wheel  2534  with an axil  2533 . The foot holder  2504  may comprise Velcro  2525  to attach to the carriage  2506 . The bearing rail  2517  and the rolling surface  2515  may comprise front  2535  and rear  2536  supports attached to the SUP  2500 . The axils of the wheels  2534  and  2509  may be seen from the side as  2533  and  2512 , respectively. 
       FIG. 26A  is a rear-end view of the thrust assembly of  FIG. 26B , where  FIG. 26B  is a side view of a useful embodiment of another thrust assembly. A right-foot carriage  2606  rolls on wheels  2608 ,  2616 , and  2630  contained by upper and lower linear rails, much like a garage door&#39;s wheels roll through a retaining channel.  FIG. 26A  provides optional upper rails  2614  and  2615  to prevent the foot carriage  2606  from coming off the lower rails  2624  and  2632 . Typically there is a similar left-foot carriage, but for clarity, it is not shown in  FIGS. 26A-26B . A thrust paddle  2613  extends from the foot carriage  2606  through openings, such as slots, along the SUP  2600  having additional sections  2601  and  2602 . The thrust paddle  2613  may rotate relative to the foot carriage  2606 , and the rotation of the thrust paddle  2613  may be impeded by limit stops. In  FIG. 26B , thrust paddles  2613  and  2625  have limit stops  2629  and  2628 , respectively. In this way, the thrust paddles  2613  and  2625  may be used to apply force against the water  2603  to propel the SUP  2600  forward (i.e., to the right in  FIG. 26B ). The thrust paddles  2613  and  2625  may be linked together by a tie rod  2622  by revolute joints  2623  and  2626 , respectively. As the rider slides their feet alternately forward and rearward, similar to a Nordic snow skier, thrust paddles in contact with the water  2603  apply force against the water  2603  to move the SUP  2600  forward. 
     The rider typically places their feet on the carriage  2606 . The carriage  2606  may comprise a foot holder  2604  with a foot support  2605 . The foot holder  2604  may comprise a water sock or a boot. The carriage  2606  connects to the wheels  2608  and  2616  by axils  2607  and  2617 , respectively. The axils  2609  and  2618  of the wheels  2608  and  2616  connect to the paddle supports  2610  and  2619 , and may be seen from the sides as axils  2611  and  2620 , respectively. The paddle supports  2610  and  2619  connect to the paddle  2613  by revolute joints  2612  and  2621 . 
       FIG. 26B  provides a front right thrust paddle  2625  with revolute joint  2627  and limit stop  2628 , as well as a front right wheel  2630  with an axil  2631 . The axils of the wheels  2630  and  2608  may be seen from the side as  2631  and  2611 , respectively. 
       FIG. 27.1  is a side view of a useful embodiment of another thrust assembly where the rider may stand sideways on the SUP  2700 , like a snowboarder stands on a snowboard, with one foot near the front of the SUP  2700  on the foot platform  2701  and one foot near the back of the SUP  2700  on the foot platform  2702 . As the rider rocks  2703  between their front and back feet, the flipper  2704 , which may be flexible, rotates up and down  2705  and provides forward thrust  2706  (i.e., to the left in the figure). The foot support is shown connected to the flipper  2704  by a pulley  2707  with pulley belt  2708 ; although, any convenient connection may be used. 
       FIG. 27.2  is a side view of a useful embodiment of another thrust assembly where the rider may stand sideways on the SUP  2709 , like a snowboarder stands on a snowboard, with one foot near the front of the SUP  2709  on the foot platform  2710  and one foot near the back of the SUP  2709  on the foot platform  2711 . As the rider rocks  2712  between their front and back feet, the pair of flippers  2713 , which may be flexible, rotate side to side  2714  to provide forward thrust  2715  (i.e., to the left in the figure). The foot support may be connected to the flippers by a Mirage Drive  2716 ; although, any convenient connection may be used. 
       FIG. 27.3 a    is a plan view of the useful embodiment of another thrust assembly where the rider may stand sideways on the SUP  2717 . The outlines of shoes  2718  and  2719  exemplify where the rider may place their feet on the foot platforms  2720  and  2721 , but there need not be actual shoes or special foot holders. 
       FIG. 27.3 b    is a front-end view of the useful embodiment of another thrust assembly where the rider may stand sideways on the SUP  2722 . In this figure, if the rider tilts  2723  from their heels  2724  to their toes  2725 , the Bowden cable  2726 , or any functionally similar apparatus, turns  2727  the steering rudder  2728 . 
       FIG. 28A  is a side view of a useful embodiment of another thrust assembly. In the thrust assembly of  FIG. 28A , the rider&#39;s foot  2802  is resting on the foot support  2803 . Alternately, a foot holder  2802  is removably secured to the foot support  2803 , and the rider&#39;s foot is held by the foot holder  2802 . Although, only a single foot support  2803  is shown, the embodiment typically comprises two foot supports, one for each foot. When the rider (not shown) applies their weight to press down on the foot support  2803 , the thrust shaft  2804  moves downward, farther into the water  2801  though opening  2805  in the SUP  2800 . The opening  2805  may comprise a linear bearing for guiding the thrust shaft  2804 . The thrust shaft  2804  is connected at the connection point  2808  to thrust member  2807 . The rear end of the thrust member  2807  is connected at the rear connection  2810  to the mount  2809 , which is connected to the SUP  2800 . The thrust member  2807  may be rigid, but typically it is flexible. If the thrust member  2807  is rigid, the rear connection  2810  typically comprises a rotary joint. If the thrust member  2807  is flexible, the rear connection  2810  may still comprise a rotary joint; however, a rotary joint is not required. The flexibility of thrust member  2807  is indicated in  FIG. 28A  by the dashed lines  2806  showing the initial position of the thrust member  2807  before the rider presses down on the foot support  2803 . Typically there is mechanical or electromechanical apparatus that keeps the right and left foot supports 180 degrees out of phase, i.e., while one foot support is going down, the other foot support is forced up. The effect is that the rider feels like they are marching in place. Each foot support has its own thrust shaft and thrust member. As each thrust member is forced up and down by the rider alternatively transferring their weight from one foot support to the other, each thrust member directs water toward the rear of the SUP  2800 , providing a forward thrust for the SUP  2800 . 
     The rider may balance themselves using the handlebars  2811  connected to the SUP  2800  by handlebar neck  2812 . The handlebars may be mechanically or electrically connected to the steering rudder  2813 . 
       FIG. 28B  is a side view of a useful embodiment of another thrust assembly. The thrust assembly of  FIG. 28B  has one or more thrust members similar to the thrust members of  FIG. 28A ; however,  FIG. 28B  also allows the rider to assist their foot-generated thrust with arm-generated thrust. If the rider pulls back on the handlebars  2819 , the hand lever  2820  rotates clockwise about a rotary joint  2822  of a support  2821 , and so the connected slide lever  2823  also rotates clockwise. The slide lever  2823  comprises a slide member  2824  that slides in the slide track  2825  when the slide lever  2823  rotates, such that when the slide lever  2823  rotates clockwise, the slide member  2824  forces the slide track  2825  down, and accordingly, forces the thrust shaft  2804  down. Conversely, if the rider pushes the handlebars  2819 , the hand lever  2820  rotates counter clockwise about rotary joint  2822 , ultimately causing the slide member  2824  to force the slide track  2825  up, which consequently forces the thrust shaft  2804  up. Coordinated hand and leg movement by the rider can lead to optimum performance, as well as a full-body exercise. 
       FIG. 28C  is a side view of a useful embodiment of another thrust assembly. The apparatus of  FIG. 28C  is similar to the apparatus of  FIG. 28A , except that the thrust member  2814  of  FIG. 28C  is different than the thrust member  2807  of  FIG. 28A . The thrust member  2814  is not connected to the SUP  2800  at the trailing edge. The thrust member  2814  may be rigid, but typically it is flexible, like a SCUBA flipper. If the thrust member  2814  is rigid, typically the connection point  2808  comprises a return spring  2816 . Such a return spring  2816  is shown schematically as a coil spring, with one end  2818  in functional relation to the thrust shaft  2804 , and the other end  2817  in functional relation to the thrust member  2814 ; however, the return spring  2816  may comprise any convenient spring structure. Even if the thrust member  2814  is flexible, as indicated by the dashed lines  2815  in  FIG. 28C , the flexible thrust member  2814  may still comprise a return spring  2816 . In either case, the thrust member  2814  may automatically straighten to reduce drag when the rider is not pressing down on the foot support  2803 . Typically there are two separate foot supports, where each foot support has its own thrust shaft and thrust member. As each thrust member is forced up and down by the rider alternatively transferring their weight from one foot support to the other, each thrust member directs water toward the rear of the SUP  2800 , providing a forward thrust for the SUP  2800 , much like a SCUBA diver propels themselves. The thrust member  2814  may be positioned beneath the SUP  2800 , to the side of the SUP  2800 , or partially beneath and partial to the side. The SUP  2800  may also comprise a cavity in the bottom surface of the SUP  2800  so the thrust member  2814  may completely retract into the cavity. Use of such a cavity is convenient if the SUP  2800  is to be used for surfing, since drag is minimized when a wave is caught. Use of a cavity also helps protect the thrust member  2814  when the SUP  2800  is placed on a hard surface. 
       FIG. 28D  is a plan view, and  FIG. 28E  is a front-end view, of the useful embodiment of  FIG. 28A .  FIGS. 28D-28E  provide the case where left and right foot supports  2803  and  2827  are used, with left and right thrust shafts  2804  and  2828  connected to left and right thrust members  2807  and  2830 , respectively. Similarly to the foot holder  2802 , a foot holder  2826  may be secured to the foot support  2827 . To keep the left and right foot supports  2803  and  2827  180 degrees out of phase, a pulley  2834  with axil ends  2836  and  2837  is supported by a pulley mount  2835 , and employing a pulley cable  2838 , may be employed; however, any convenient mechanical or electromechanical means may be used. If programmable electromechanical means with position sensors and electromechanical position actuators are used, any desired phase between the left and right foot supports may be selected. The pulley apparatus provided by  FIGS. 28D-28E , and functional equivalences, may be similarly applied to the thrust apparatus of  FIG. 28C . 
     In  FIG. 28D , the trailing edges of thrust members  2807  and  2830  are shown to be attached only by their corners to the SUP  2800  or to the mounts  2809  and  2833 . With this design, water may flow thought the gaps  2831  and  2832  between the corners of the thrust members  2807  and  2830 . As provided in  FIG. 28D  (but not similarly provided in  FIG. 28E ), the thrust shafts  2804  and  2828  may bow out to connect to the sides  2808  and  2829  of the thrust members  2807  and  2830 . With proper support (not shown) of the foot supports to the SUP  2800 , the thrust shafts  2804  and  2828  may extend out around the sides of the SUP  2800  so there do not need to be holes  2840  and  2839  through the SUP  2800 . 
       FIG. 29.3 c    is a side view of a useful embodiment of another thrust assembly. The apparatus of this figure is similar to the apparatus of  FIG. 28B , but where only arms  2900  are used to provide thrust. Additionally, a leash  2901  may be used to support the rider  2902  when they pull  2903  against the handles  2904 . Velcro  2905  may be used to secure the leash to the rider  2902 . 
       FIG. 29.3 d    is a plan view of a useful embodiment where a throttle grip  2906  comprises a Bowden cable  2907  to control the rudder  2908 . 
       FIG. 29.4 a    is a side view of a useful embodiment of another thrust assembly, where a rigid curved rod  2909  is connected to the foot support  2910 , goes around the SUP  2911  using a pivot  2912 , and moves the thrust member  2913  up and down  2914  to provide thrust. 
       FIG. 29.4 b    is a front-end view of a useful embodiment where the two foot supports  2916  and  2917  are kept 180 degrees out of phase using a pulley  2918  and pulley cable  2919 . The pulley  2918  is supported by the SUP  2915 . The right foot support  2916  has a sliding member  2925  attached to one end of the pulley cable  2919 . The sliding member  2925  is guided by a guiding member  2926 . The pulley cable  2919  passes around the pulley  2918  and is connected to the left foot support  2917 . The left foot support is connected to a flexible flipper  2921  with a connecting member  2927 . When the left foot support  2917  is pressed down  2923  by the rider, the pulley cable  2919  rotates the pulley  2918  clockwise  2920 , and causes the right foot support  2916  to elevate  2924 . Also when the left foot support  2917  is pressed down  2923 , the connecting member  2927  forces the flexible flipper  2921 , producing thrust as the flexible flipper  2921  flexes. When the right foot support  2916  is pressed down, the pulley  2918  and pulley cable  2919  elevate the left foot support  2917 , which also elevates the flexible flipper  2921 , producing thrust. 
       FIG. 30.5 a    is a perspective view of a useful embodiment of another thrust assembly, where moving handles  3000  and  3001  forward  3002  and rearward  3003  makes a flexible flipper  3004  move side to side to provide forward thrust as well as turning. FIG.  30 . 5   b  shows an assembly comprising pulleys  3005  and  3006  and a pulley belt  3007  to keep the two handles  3008  and  3009  180 degrees out of phase, where when one handle  3008  is being pushed forward  3010 , the other handle  3009  moves backward  3011 . 
       FIG. 30.6 a    is a side view of a useful embodiment of another thrust assembly, where a rigid curved rod  3012  is connected to the foot support  3013  and to a hand lever  3014  with a sliding slot  3015 , where the curved rod  3012  goes around the SUP  3016  using a pivot  3017 , and moves the thrust member, shown here as a flexible flipper  3018 , up  3019  and down  3020  to provide thrust.  FIG. 30.6 b    is similar to  30 . 6   a , except the hand lever  3021  is connected to the curved rod  3022  using a tie rod  3023  with rotary joints  3024  and  3025  on each end. 
       FIG. 30.7  is a plan view of a useful embodiment of another thrust assembly, where rocking handlebars  3026  back  3027  and forth makes a flexible rear flipper  3028  move side to side to provide forward thrust as well as turning. In this figure, an assembly comprising pulleys  3029  and  3030  and a pulley belts  3031  is used to mechanically connect the handlebar shaft  3032  with the flipper rotary joint  3033 . 
       FIG. 31.8 a    is a side view of a useful embodiment of another thrust assembly, where the up and down  3110  motion of the foot support  3109  is constrained by a four-bar mechanism. The four-bar mechanism comprises members  3105 ,  3106 ,  3107 , and  3108 . The foot support  3109  is fastened to the member  3105 , and the member  3107  is fastened to the SUP  3115 . In this embodiment, a pulley  3111  is supported by the SUP  3115 , and the pulley cable  3112  is connected at two points on the member  3108 , whereby rocking of the member  3108  about the pivot  3138  causes the pulley  3111  to rotate  3114 , which then also causes the flexible flipper  3113  to rotate up and down, providing thrust. 
       FIG. 31.8 b    is a front-end view of a useful embodiment, such as a portion of the embodiment of  FIG. 31.8 a   , where the two foot supports  3116  and  3117  are kept 180 degrees out of phase using a pulley  3118  and pulley cable  3120 . The pulley  3118  is supported by the SUP  3121 . The right foot support  3116  is attached to one end of the pulley cable  3120 . The pulley cable  3120  passes around the pulley  3118  and is connected to the left foot support  3117 . When the left foot support  3117  is pressed down by the rider, the pulley cable  3120  rotates the pulley  3118  clockwise, and causes the right foot support  3116  to elevate. When the right foot support  3116  is pressed down, the pulley  3118  and pulley cable  3120  elevate the left foot support  3117 . 
       FIG. 31.9  is a side view of a useful embodiment of another thrust assembly, where rocking handlebars  3100  back and forth  3101  makes a flexible flipper  3102  move side to side  3103 , using a direct shaft connection  3104 , to provide forward thrust as well as turning. 
       FIG. 31.10 a    is a front view of a useful embodiment for keeping the right  3122  and left  3123  foot supports moving 180 degrees out of phase using a pulley  3127  and pulley cable  3128 , while simultaneously moving a flexible flipper  3124  up and down to provide forward thrust. In this figure, a rack  3125  and pinion  3126  is provided; however, any other functionally equivalent apparatus may be used. 
       FIG. 31.10 b    is a side view of the flexible flipper  3124  of  FIG. 31.10   a.    
       FIG. 31.10 c    is a front view of a useful embodiment for keeping the right  3139  and left  3140  foot supports moving 180 degrees out of phase using a four-bar mechanism, while simultaneously moving a flexible flipper  3141  up and down to provide forward thrust. The four-bar mechanism comprises members  3144 ,  3145 ,  3146 , and  3147 . In this figure, the four-bar mechanism is connected to a rack  3142  and pinion  3143 ; however, any other functionally equivalent apparatus may be used. The member  3147  is connected to the pinion  3143 , and both rotate around the axis  3148  which is supported by the SUP  3149 . The rack  3142  is connected to the flexible flipper  3141 . When the rider presses down on the foot support  3140 , the members  3147  and  3145  rotate counter clockwise, as does the pinion  3143 , and the foot support  3139  elevates. The pinion  3143  is meshed with the rack  3142  and causes it and the flexible flipper  3141  to elevate, providing thrust. Similarly, when the rider presses down on the foot support  3139 , the flexible flipper  3141  lowers, again providing thrust. 
       FIG. 31.11  is a side view of a useful embodiment of another thrust assembly where the rider  3129  may stand, and by rocking the handles  3130  and  3131  forward  3132  and backward  3133 , the pair of flippers  3134  and  3135 , which may be flexible, rotate side to side  3136  to provide forward thrust (i.e., to the left in the figure). The handle levers may be connected to the flippers  3134  and  3135  by a Mirage Drive  3137 ; although, and convenient connection may be used. 
       FIG. 32  is a side view of a useful embodiment of another thrust assembly, where pushing and pulling  3138  on the handlebars makes a flexible flipper  3139  move up  3140  and down  3141 , to provide forward thrust as well as turning  3142 . 
       FIG. 33.1  is a side view of a useful embodiment of another thrust assembly, where when the rider  3300  stomps down  3301  on the foot support  3302 , fluid is compress and expelled  3304  from a pump  3303 , providing forward thrust. The pump  3303  may comprise an impeller, and the impeller may be rotated by a pedaling motion and/or a stomping motion. The fluid may be water taken in through an intake  3305  below the waterline  3306 , or the fluid may be air taken through an intake  3307  above the waterline  3306 . 
       FIG. 33.2  is a side view of a useful embodiment of another thrust assembly, where the SUP  3308  comprises a battery  3309 , where the battery  3309  may be located in a water tight compartment in the SUP  3308  (as shown), or on the SUP  3308 , and the battery  3309  provides electrical power to a trolling motor  3310 , providing forward thrust and steering. Although not shown, the trolling motor column  3311  may collapse down for transport and storage, like the steering column of a Razor scooter. The trolling motor and propeller  3312  may rotate up into a cavity (not shown) in the SUP  3308 . 
       FIG. 33.3  is a side view of a useful embodiment of another thrust assembly, where right  3313  and left  3314  foot supports each comprise a plurality of retractable thrust fins  3315  and  3316 , respectively, to help propel the SUP  3320 . Each foot  3317  and  3318  of the rider  3319  is supported by a foot support  3313  or  3314 , respectively, which the rider  3319  can move relative to the SUP  3320 . When a foot support  3313  is moved rearward  3323 , the thrust fins  3315  extend downward into the water; and when a foot support  3314  is moved forward  3324 , the thrust fins  3316  retract to minimize water resistance. The SUP  3320  may comprise steering as shown where a steering handle  3321  steers a rudder  3322  to turn the SUP  3320 . 
       FIG. 34A  is a side view of a useful embodiment of another thrust assembly, where the rider  3400  pulls rearward  3401  against a handle  3402  to move thrust fins  3403  rearward  3404  to generate forward thrust  3405  for the SUP  3406 . The rider  3400  may press their shin  3407  against a shin support  3408  to provide the reaction force to the rearward pulling  3401  against the handle  3402 . 
       FIG. 34B  is a side view of a useful embodiment of another thrust assembly, where the rider  3409  pushes forward  3410  against a handle  3411  to move thrust fin  3412  rearward  3413  to generate forward thrust  3414  for the SUP  3415 . The rider  3409  may press their leg  3416  against a leg support  3417  to provide the reaction force to the forward pushing  3410  against the handle  3411 . 
       FIG. 34C  is a side view of a useful embodiment of another thrust assembly, where fluid pump  3418  comprising an impeller/blower cage  2428  is powered by a rider to generate propulsion  3419  from the rear of the SUP  2427 . Water may enter the pump  3418  from a water intake port on the front  3420 , side  3421 , or bottom  3422 . In this figure, the rider uses pedals  3423  mechanically coupled using meshing gears  3424  and  3425  to rotate the pump  3418  about its rotary axis  3426 . 
       FIG. 34D  is a plan view of the useful embodiment of  FIG. 34C . 
       FIG. 34E  is a side view of a useful embodiment of another thrust assembly, where a bicycle frame  3429  is mounted to an SUP  3430  and used to steer and generate propulsion. The front forks  3431  of the bicycle frame  3429  may be set into a socket  3432  for the front steering rudder  3433 . The rider-powered rear axil  3434  of the bicycle frame  3429  may be mechanically coupled to rotate  3435  a propulsion device to propel the SUP  3430  forward  3436 , including paddles  3437 , a propeller, impeller, Mirage Drive, and the like. 
       FIG. 34F  is a side view of a useful embodiment of another thrust assembly, where an SUP  3438  is powered by an electric battery  3439  connected to an electric motor  3440  with propeller  3441  that is turned by handlebars  3442 .  FIG. 34G  is a side view of the useful embodiment of  FIG. 34F  where the handlebars  3442  are folded down against the SUP  3438 , and the electric motor  3440  with propeller  3441  is retracted up into a cavity  3443  in the SUP  3438 . When the electric motor  3440  with propeller  3441  is not retracted up, the cavity  3443  in the SUP  3438  may be covered by a removable plug  3444 . The electric battery  3449  may be placed on the SUP  3438  in a location as a counterweight to the rider. 
       FIG. 35A  is a side view of a useful embodiment of another thrust assembly, where a rider of an SUP  3500  can stand, place each hand on handles  3501  and  3502 , and steer by turning  3503  an electric motor  3504  axially connected  3505  to the handles  3501  and  3502 . 
       FIG. 35B  is a side view of a useful embodiment of another thrust assembly, where a rider of an SUP  3506  can stand, place each hand on handles  3507  and  3508 , and steer by turning  3509  an electric motor  3510  connected to the handles  3507  and  3508  using a Bowden cable  3511 . One end of the Bowden cable tendon  3512  is attached to a moment arm  3513  on the handle shaft  3514 , and the other end of the Bowden cable tendon  3515  is attached to a moment arm  3516  on the electric motor base axil  3517 . The handle shaft  3514  may be mounted into the hand-carry slot in the SUP  3506  for easy retrofitting of a stock SUP, and the electric motor base  3518  may be mounted into the fin slot of the SUP  3506 , again for easy retrofitting of a stock SUP. 
       FIG. 35C  is a plan view of a useful embodiment of another thrust assembly, where a rider of an SUP  3519  can stand, place each hand on handles  3520  and  3521 , and steer by turning  3522  one or more rudders  3523  and  3524  connected to the handles  3520  and  3521  using a Bowden cable  3525 . One end of the Bowden cable tendon  3526  is attached to a moment arm  3527  on the handle shaft  3528 , and the other end of the Bowden cable tendon  3529  is attached to a first rudder  3523  with axis of rotation  3534 . When a second rudder  3524  is used having an axis of rotation  3535 , the first rudder  3523  may be mechanically connected to the second rudder  3524  by a tie rod  3530 . In this figure, the electric motor  3531  with propeller  3532  is not turned by the handle shaft  3528 , but the handles turn the rudders  3523  and  3524  behind the motor propeller  3532 . The electric motor  3531  is electrically connected to an electrical battery  3533 . The handle  3520  may comprise a throttle to adjust the electrical current to the electric motor  3531 . 
       FIG. 35D  is a side/perspective view of the useful embodiment of  FIG. 35C . 
       FIG. 36A  is a plan view of a useful embodiment of another thrust assembly, where a left foot support  3600  and a right foot support  3601  are guided by linear bearings  3602  and  3603 , respectively, on an SUP  3604 . The foot supports  3600  and  3601  are connected by a pulley cable  3615  that passes around the pulleys  3605  and  3606  mounted on the SUP  3604  that rotate propellers. The pulley arrangement provides that when the foot support  3600  is moving forward  3616 , the pulleys  3605  and  3606  each rotate clockwise  3618 , and the foot support  3601  must move backward  3617 , and vice versa. 
       FIG. 36B  is a plan/side view of the useful embodiment of  FIG. 36A  providing the pulleys  3605  and  3606  mechanically connected to the propellers  3607  and  3608 , respectively. The plan view of the pulleys  3605  and  3606  is provided, and for illustrative purposes, the view of the propellers  3607  and  3608  is a side view, where the axes of rotation  3609  and  3610  of the pulleys  3605  and  3606 , respectively, is coaxial with the rotary axils  3611  and  3612 , respectively, extending to the motor housings  3613  and  3614 , respectively, where the rotary axils  3611  and  3612  cause the propellers  3607  and  3608 , respectively, to rotate  3619 . Whereas two propellers  3607  and  3608  are shown in these figures, only one propeller is necessary to provide propulsion. 
       FIGS. 36C to 36F  are different views of a motor housing  3620  with a flexible fin  3621  for propulsion.  FIG. 36C  is a side view of the motor housing  3620  with the flexible fin  3621 . A torsionally stiff axil  3622  extends from the motor housing  3620 , such that the flexible fin  3621  is attached to the axil  3622 . The flexible fin  3621  comprises a relatively stiff spine  3623  along the edge  3624  nearest the motor housing  3620 . Note that if the propellers  3607  and  3608  are rigid, then they must rotate in only one direction to provide forward propulsion, regardless of the direction of rotation of the pulleys  3605  and  3606 . In contrast, the flexible fin  3621  of  FIGS. 36C to 36F  provides forward propulsion regardless of the direction of rotation of its axil  3622 . As the axil  3622  rotates, the portion  3625  of the flexible fin  3621  that is farthest from the axil  3622  and from the spine  3623  will flex the most, creating a curved contour  3626  that always pushes water in such a way that provides propulsion with a propulsion vector component  3627  along the direction of the axil  3622 . 
       FIG. 36D  is an end view of the flexible fin.  FIG. 36E  is a plan view of the flexible fin  3621  rotating clockwise in  FIG. 36D , where the corner  3625  is flexing away from the axil  3622  and spine  3623 . Similarly,  FIG. 36F  is a plan view of the flexible fin  3621  rotating counterclockwise in  FIG. 36D . 
       FIG. 37A  is a perspective view of a useful embodiment of another thrust assembly, where a left foot support  3700  and a right foot support  3701  are guided by linear bearings  3702  and  3703 , respectively, on an SUP  3704 . Each foot support is connected to one or more propulsion fins. In  FIG. 36A , the left foot support  3700  is connected  3705  to an array of retracted propulsion fins  3706 ; and the right foot support  3701  is connected  3707  to an array of extended propulsion fins  3708 . When the left foot support  3700  is slid forward by the rider, the propulsion fins  3706  retract to minimize water drag; when the right foot support  3701  is slid rearward by the rider, the propulsion fins  3708  are extended to press against as much water as possible. When multiple propulsion fins are used for a single foot support, the propulsion fins may be connected by a connecting rod  3809  so they all move in unison. 
       FIG. 37A  also shows handlebars  3710  with left  3711  and right  3712  control levers. As shown, the handlebars  3710  use a Bowden cable  3713  to turn the rear rudder  3714  for steering. The one end  3715  of the Bowden cable tendon is connected to a lever arm  3716  on the handlebar shaft  3717 , and the other end  3718  of the Bowden cable tendon is connected to a lever arm  3719  on the rudder  3714  or rudder axil  3720 . So, when the handlebars are turned, the Bowden cable tendon  3715  translates relative to the Bowden cable sheath  3721  that is attached to the SUP  3704 , and transmits rotary motion from the handlebars  3710  to the rudder  3714 . 
     In  FIG. 37A , the control levers  3711  and  3712  may be used to control whether the propulsion fins are extended  3708  or retracted  3706 . As shown, a Bowden cable  3724  is used, where one end  3722  of the Bowden cable tendon is connected to the right control lever  3712 , and the other end  3723  of the Bowden cable tendon is connected to a propulsion fin  3708  or to the connecting rod  3709 . So, the position of the control lever controls the position of the propulsion fins. In typical operation, the rider would activate the right control lever  3712  to extend the right propulsion fins  3708  and then slide the right foot support  3701  rearward to generate forward thrust. Simultaneously, the left control lever  3711  would be in the position to retract the left propulsion fins  3707  so the SUP  3704  may glide forward with minimum water resistance. The process is then alternated so the left foot platform provides the thrust. If both control levers  3711  and  3712  are simultaneously used to lower both sets of propulsion fins  3706  and  3708 , braking of the SUP  3704  will occur. If only the right control lever  3711  is used to lower the propulsion fins  3708  on the right side, but the right foot support  3701  is not simultaneously slid rearward, braking will occur only on the right side, causing the SUP  3704  to turn to the right, similarly to how a bulldozer turns. The entire apparatus provided by  FIG. 37A  may be secured to the SUP  3704  using suction, adhesive, screws, etc. 
       FIG. 37B  is an end view of a useful embodiment of another thrust assembly, where the left and right propulsion fins  3725  and  3726  are positioned to the side of the SUP  3741  and to the sides of the left and right foot supports  3727  and  3728 , respectively. The left and right foot supports  3727  and  3728  are connected by left and right connectors  3729  and  3730  to the left and right propulsion fins structures  3731  and  3732  that comprise the left and right propulsion fins  3725  and  3726 , respectively. The left and right foot supports  3727  and  3728  are shown in this figure to be supported by left and right linear guides  3733  and  3734 , respectively. The propulsion fins  3725  and  3726  are rotationally connected by axils  3735  and  3736  to the propulsion fin structures  3731  and  3732 , respectively. Left and right connecting rods  3737  and  3738  connect sets of left and right propulsion fins  3725  and  3726 . Also shown are handlebars  3739  and a rudder  3740 . 
       FIG. 37C  is an end view of an alternate to the useful embodiment of  FIG. 37B , where the left and right propulsion fins  3725  and  3726  are positioned underneath the SUP  3741  and underneath the left and right foot supports  3727  and  3728 , respectively. 
       FIG. 37D  is a side view of a useful embodiment of a foot support, where a flexible foot holder  3742 , such as a neoprene boot, is fastened using Velcro  3743  to a flexible layer  3744  that is fastened by a snap  3745  to a rigid foot support  3746  that may be connected to a component of an SUP. The Velcro  3743  provides one manner to disconnect the foot holder  3742  from the rigid foot support  3746 , and the snap  3745  provides another manner. The snap  3745  placed near the toe end  3747  of the flexible layer  3744  also insures that only the front portion of the flexible layer  3744  is attached to the rigid foot support  3746 . This allows the rider to lift their heel  3748  as desired, such as occurs with a Nordic snow ski binding, yet still provides a secure tangential connection. 
       FIG. 37E  is a side view of a useful embodiment of a foot support, where a flexible foot holder  3749 , such as a neoprene boot, is fastened  3755  using cotton Velcro  3750  near the toe portion  3751  of the foot holder  3749 , and hook Velcro  3756  also near the front portion  3752  of a rigid foot support  3753  that may be connected to a component of an SUP. The cotton Velcro  3750  placed near the toe end  3751  of the flexible foot holder  3749  allows the rider to lift their heel  3754  as desired, such as occurs with a Nordic snow ski binding, yet still provides a secure tangential connection, but with removable with a quick release. 
       FIG. 37F  is a plan view of the useful embodiment of the foot support of  FIG. 37E . 
       FIG. 37G  is a side view of the useful embodiment of the foot support of  FIG. 37E  where the cotton Velcro  3750  is fastened to the hook Velcro  3756  while still allowing the heel  3754  to be lifted. 
       FIG. 37H  is a side view of a useful embodiment of a foot support, where a shoe  3757 , such as a workout shoe, is strapped using straps  3758  to a foot support flexible layer  3759  comprising Velcro near the toe region  3760 , such as cotton Velcro  3761 . The cotton Velcro  3761  is for fastening to hook Velcro also near the front portion of a rigid foot support that may be connected to a component of an SUP. The cotton Velcro  3761  placed near the toe end  3760  of the flexible foot support flexible layer  3759  allows the rider to lift their heel  3762  as desired, such as occurs with a Nordic snow ski binding, yet still provides a secure tangential connection, but with removable with a quick release. 
       FIG. 38A  is a perspective view of a useful embodiment of another thrust assembly, where a portion  3800  of the rider  3801  is positioned below the water level  3802 , but the rider  3801  remains substantially dry inside a container  3803 , where the container is largely below the water surface  3802 . The embodiment provides a submarine-ish vehicle that is largely submerged, but keeps the rider&#39;s head above the waterline. The rider may stand on a surface to propel. The rider  3801  may use any of the thrust assemblies disclosed, such as the thrust assembly  3804 , or an alternate thrust assembly. 
       FIG. 38B  is a plan view of the useful embodiment of  FIG. 38A . 
       FIG. 39A  is a side view of a useful embodiment of another thrust assembly, where the rider  3900  places their left  3901  and right feet  3902  on the left  3903  and right  3904  foot supports and faces to the side of the SUP  3905 , like a snowboarder stands on a snowboard. The left  3903  and right  3904  foot supports are connected together by left  3906  and right  3907  rocker arms that rotate together around a rotary bearing  3908 . One of the rocker arms, such as the left rocker arm  3906  is connected by a push rod  3909  to a flexible flipper  3910 . The flexible flipper  3910  typically does not rotate relative to the push rod  3909 , but the flexible flipper  3910  flexes. When the rider  3900  pushes down  3925  with their left foot  3901  on the left foot support  3903 , the push rod  3909  lowers  3926  the flexible flipper  3910  and generates thrust to propel the SUP  3905  to the right  3911 . Similarly, when the rider  3900  pushes down with their right foot  3902  on the right foot support  3904 , the push rod  3909  raises the flexible flipper  3910 , and again generates thrust to propel the SUP  3905  to the right  3911 . Accordingly, thrust is achieved through by the rider rocking from one foot to the other. Typically, when the left foot support  3903  is all the way up (i.e., the right foot support  3904  is all the way down), the flexible flipper  3910  can lie flush with the bottom of the SUP  3905 . The rocker arms  3906  and  3907  may also be connected to a Mirage Drive. 
     Steering may be accomplished using hand-held controllers. In  FIG. 39A , the left  3912  and right  3913  hand-held controllers comprise left  3914  and right  3915  Bowden cables, respectively. For the left hand-held controller  3912 , one end  3916  of the tendon is attached to a movable gripper  3917 , and the associated end of the sheath  3918  is attached to a stationary gripper  3919 . When the rider closes their grip, the movable gripper  3917  is pulled away from the sheath  3918  and translates the tendon  3916 . The other end  3920  of the tendon is attached to a lever arm  3921  attached to a rudder  3922  or rudder axil  3923 , and the associated end of the sheath  3924  is attached to the SUP  3905 . Accordingly, when the rider closes their grip, the rudder  3922  is turned. The right hand-held controller  3913  operates similarly to turn the rudder  3922  the other way. If either of the hand-held controllers turns the rudder 90 degrees, the SUP  3905  will brake. 
       FIG. 39B  is a side view of a useful embodiment of another thrust assembly, where the rider places their left and right feet on the left  3927  and right  3928  foot supports and faces to the side of the SUP  3929 , like a snowboarder stands on a snowboard. The left  3927  and right  3928  foot supports are connected together by left  3930  and right  3931  rocker arms that rotate together around a rotary bearing  3932 . The left rocker arm  3930  is connected by a push rod  3933  to a flexible flipper  3934 . The flexible flipper  3934  may rotate relative to the SUP  3929  via a rotary pinned joint  3935  connected to a flipper support structure  3941  attached to the SUP  3929 . The push rod  3933  has a pinned end  3937  to the left rocker arm  3930 , and a pinned end  3938  to the flexible flipper  3934 . When the rider pushes down  3936  with their left foot on the left foot support  3927 , the push rod  3933  rotates the flexible flipper  3934  downward and generates thrust to propel the SUP  3929  to the right. Similarly, when the rider pushes down with their right foot on the right foot support  3928 , the push rod  3933  rotates the flexible flipper  3934  upward, and again generates thrust to propel the SUP  3929  to the right. There may be a second flexible flipper  3939  that is connected to the right foot support  3928  by a right push rod  3940 , where this second flexible flipper  3939  rotates upward when the first flexible flipper  3934  rotates downward, and vice versa. Accordingly, thrust is achieved through by the rider rocking from one foot to the other. The rocker arms  3930  and  3931  may also be connected to a Mirage Drive. 
       FIG. 39C  is an end view of the useful embodiment of  FIG. 39B , where the push rods, such as the push rod  3933 , extend around to the side of the SUP  3929  to reach the flexible flippers, such as flexible flipper  3934 , which is beneath the SUP  3929 . 
       FIG. 39D  is a plan view of the flexible flipper of the useful embodiment of  FIG. 39B , and  FIG. 39E  is a plan view of the flexible flipper of the useful embodiment of  FIG. 39A . 
       FIG. 39F  is a plan view of a useful embodiment of the turning structure of  FIG. 39A  that uses a Bowden cable  3942 . A hand-held controller comprises a thumb lever  3943  and a finger lever  3944  that rotate relative to each other by a rotary joint  3945 . The thumb lever  3943  supports one end of the sheath  3946  of the Bowden cable  3942 , and the finger lever  3944  supports one end  3947  of the tendon of the Bowden cable  3942 . Alternately, the sheath  3946  may be supported by the finger lever  3944 , and tendon  3947  may be supported by the thumb lever  3943 . When the rider squeezes  3952  the thumb lever  3943  toward the finger lever  3944 , the tendon  3947  is translated  3961  relative to the sheath  3946 . The other end  3948  of the sheath is connected to the SUP, and the associated end  3949  of the tendon is attached to the rudder  3950  or to a lever arm  3951  attached to the rudder. So, when the rider squeezes  3952  their thumb toward their fingers, the end  3949  of the tendon is translated  3962  which rotates  3963  the lever arm  3951  and the rudder  3950  to one side  3953 , causing the SUP to turn. 
       FIG. 39G  is a plan view of a useful embodiment of the turning structure of  FIG. 39A  that uses a Bowden cable  3954 . One end  3955  of the tendon is attached to a movable gripper  3956 , and the associated end of the sheath  3957  is attached to a stationary gripper  3958 . When the rider closes their grip, the movable gripper  3956  is pulled away from the sheath  3957  and translates the tendon  3955 . The other end  3959  of the tendon is typically attached to a lever arm attached to a rudder or to the rudder axil, and the associated end of the sheath  3960  is attached to the SUP. Accordingly, when the rider closes their grip, the rudder is turned. 
       FIG. 39H  is a combination side/perspective view of a useful braking embodiment comprising a brake lever  3964  and a Bowden cable  3965 . When the brake lever  3964  is squeezed  3969 , the tendon  3966  that is attached  3970  to the braking fin  3967  causes the braking fin  3967  to rotate  3968  to an orientation presenting more surface area to the direction of travel, and hence providing more resistance to motion and producing braking. 
       FIG. 39I  is a perspective view of a useful embodiment of another thrust assembly, where the left  3971  and right  3972  foot supports are constrained by a constraint assembly to rotate in opposite directions. Each foot support  3971  and  3972  is shown controlling the movement of a separate flexible flipper  3973  and  3974 , respectively; although, only one flexible flipper is necessary. The left  3971  and right  3972  foot supports are positioned above the SUP  3982 , and the flexible flippers  3973  and  3974  are positioned in the water. The dashed shoe outlines  3975  and  3976  are intended to indicate where the rider typically places their feet. When the rider presses down  3988  with their foot on the right foot support  3972 , the right axil  3977  rotates the right pulley  3978  counterclockwise  3979 . The pulley cable  3980  that passes around the right pulley  3978  rotates the rear pulley  3981  clockwise, and rotates the left pulley  3983  clockwise  3984 , and rotates the front pulley  3985  counterclockwise  3986 . Since the left foot support  3971  is connected to the left pulley  3983  by the left axil  3987 , the right foot support  3972  can only be rotated down  3988  if the left foot support  3971  is rotated up  3989 . The right push rod  3990  connects the right foot support  3972  to the right flexible flipper  3974 . Accordingly, when the right foot support  3972  is rotated down  3988 , the right flexible flipper  3974  is pushed down and provides thrust toward the right in the figure. Similarly, the left foot support  3971  may be connected to a left flexible flipper  3973  by a left push rod  3991 . Note that although  FIG. 39I  shows a structure similar to  FIG. 39B  where the right flexible flipper  3974  pivots around the flipper support structure  3992  attached to the SUP  3982 , the right push rod  3990  may operate similarly to the push rod  3909  of  FIG. 39A  and  FIG. 39E , where the right flexible flipper  3974  does not rotate relative to the right push rod  3990 , but the flexible flipper  3974  flexes to provide thrust. 
     In general, the thrust assemblies, steering, and braking apparatuses provided may be positioned on a standard SUP, such as to the hand-carry hole, and locked in place. Adhesive or suction may be used for mounting. Push rods may go around the side of a standard SUP, or can go through the SUP. A Bowden cable may use a Teflon sheath with a Dacron tendon. 
       FIG. 40A  is a side view of a useful embodiment for wirelessly controlling a rudder  4000  of an SUP. One end of an SUP paddle  4001  may have control buttons  4002  and a wireless transmitter, and the shaft  4003  of the SUP paddle may have a handle  4004  that rotates around the SUP paddle, where the angle of rotation is detected and wirelessly transmitted to the rudder  4000 . The rudder  4000  may rotate about an axis  4005  relative to an SUP mount  4006 . 
       FIG. 40B  is a side view of a useful embodiment for remotely mechanically controlling a rudder  4007  of an SUP. The shaft  4008  of the SUP paddle has a handle  4009  that rotates  4016  around the SUP paddle, where the angle of rotation is mechanically transmitted to the rudder  4007  by a Bowden cable tendon-sheath assembly  4009 . One end  4010  of the Bowden cable tendon is connected to the lever arm  4011  on the SUP paddle, and the other end  4012  of the tendon is connected to the lever arm  4013  attached to the axel  4014  of the rudder  4007 . When the handle  4009  rotates  4016  relative to the SUP paddle shaft  4008 , the rudder  4007  rotates about the axel  4014  relative to an SUP mount  4015  that may be inserted into the rudder slot in the SUP. 
       FIG. 41A  is a side view of a useful embodiment of another thrust assembly, where thrust is provided by a paddle wheel  4100  which may be located to the rear  4101  or side of an SUP  4102 . Components for generating thrust, as well as handles  4103  for steering and brake levers  4120  for braking, may be fastened to a surface  4104  that is then fastened to an existing SUP  4102 , such as by straps  4105  or screws. A boot  4106  is shown to illustrate where a rider&#39;s foot is typically placed on a foot support  4107 . The foot support  4107  can pivot relative to the SUP  4102  around a pivot  4108  near the front portion  4109  of the foot support  4107 . A push rod  4110  connects the rear portion  4121  of the foot support  4107  to a drive wheel  4111  with pinned pivot joints  4112  and  4113 , such that when the rider presses down with their heel  4114 , the drive wheel  4111  rotates clockwise  4115 , like a piston rotates a crankshaft. Similar to a bicycle with pedals, typically there is one foot support for each foot, and each foot support with its own push rod, and the foot supports are connected to opposite ends of the drive wheel  4111 , like pedals are connected to opposite ends of a drive sprocket on a bicycle. As the rider alternately applies their weight to one foot support  4107 , and then to the other foot support, the drive wheel  4111  turns. Again, similar to a bicycle, the drive wheel  4111  is connected to the paddle wheel  4100  by a flexible loop  4116 , such as a chain or pulley belt, such that when the drive wheel  4111  is turned, it causes the paddle wheel  4100  to turn  4117 . The paddle wheel  4100  may be connected by a connecting member  4122  to the rudder housing  4118 , that also holds the rudder  4119 , and that is connected to the standard rudder slot on the bottom rear portion of the SUP  4102 . 
       FIG. 41B  is a side view of a useful embodiment of another thrust assembly, where thrust is provided by a paddle wheel  4123  which may be located to the rear  4124  or side of an SUP  4125 . Also shown are components for generating thrust, as well as handles  4126  for steering and brake levers  4127  for braking, fastened to an existing SUP  4125 . The foot support  4127  can pivot relative to the SUP  4125  around a pivot  4128  near the front portion  4129  of the foot support  4127 . A curved member  4130  attached to the foot support  4127  guides a roller bearing  4131 , which is attached to a drive wheel  4132 , in a circular trajectory. When the rider presses down with their heel  4133 , the drive wheel  4132  rotates clockwise  4134 . Similar to a bicycle with pedals, typically there is one foot support for each foot, and each foot support with its own curved member guiding a roller bearing, and the roller bearings are connected to opposite ends of the drive wheel  4132 , like pedals are connected to opposite ends of a drive sprocket on a bicycle. As the rider alternately applies their weight to one foot support  4127 , and then to the other foot support, the guide members alternately apply downward force to the roller bearings on opposite ends of the drive wheel  4132 , causing the drive wheel  4132  to turn  4134 . Again, similar to a bicycle, the drive wheel  4132  is connected to the paddle wheel  4123  by a flexible loop  4135 , such as a chain or pulley belt, such that when the drive wheel  4132  is turned, it causes the paddle wheel  4123  to turn  4136 . The paddle wheel  4123  may be connected by a connecting member  4137  to the rudder housing  4138 , that also holds the rudder  4139 , and that is connected to the standard rudder slot on the bottom rear portion of the SUP  4125 . The paddle wheel  4123  may be partially covered by a fender  4140  to prevent water from splashing onto the SUP  4125  or the rider. 
       FIG. 41C  is a plan view of a useful embodiment of a thrust assembly comprising one or more paddle wheels for providing thrust, where the paddle wheels may be located to the rear  4141  of an SUP  4142 , to the left side  4143 , to the right side  4144 , or to the side and set back  4145 . Various paddle wheel locations for generating thrust, as well as handles  4146  for steering, are provided. 
       FIG. 42A  is a side view of a useful embodiment of another thrust assembly, where a drive sprocket  4200  is connected to a rear sprocket  4201  by a chain  4202  or cable, and the rear sprocket  4201  uses right-angle gears  4203  and  4204  to rotate  4205  a propeller  4209  to provide thrust. The drive sprocket  4200  may be rotated  4206  by the rider of an SUP  4212  using foot supports such as are described in detail in other figures. The drive sprocket  4200  may have an axil  4207  with bearings  4208 , and the propeller  4209  may have a propeller shaft  4210  with a bearing  4211 . 
       FIG. 42B  is a side view of a useful embodiment of a braking assembly, where the heel  4213  of a rider pushes on a pad  4214  that rubs on a rotating element  4215  that is attached  4216  to one or more paddle wheels  4217 . As the rider applies more of their weight to the pad  4214 , the pad exerts more friction to the rotating element  4215  to restrict it from turning, and thus restricting the attached paddle wheels  4217  from turning, which provides braking for a moving SUP  4218 . 
       FIG. 42C  is a side view of a useful embodiment of another braking assembly, where when the rider presses down  4228  their foot  4229  on a foot support  4219  connected by a brake rod  4220  to a brake fin  4221 , causing the brake fin  4221  to rotate  4222  about a pivot  4223  to a lower position  4224  to increase drag force to provide braking. The brake fin  4221  may be attached to a rudder housing  4225  that is attached to the rudder slot on the SUP  4226 , and that is also attached to the rudder  4227 . 
       FIG. 43A  is a plan view of a useful embodiment of another thrust assembly, where left  4300  and right  4301  foot supports slide along left  4302  and right  4303  slide paths, respectively, on an SUP  4308 . Foot supports  4300  and  4301  are connected to rotatable thrust paddles  4304  and  4305 , respectively. When the left foot support  4300  is sliding forward  4306 , the left paddle  4304  is rotated above the water level so there is no resistance to motion applied to the paddle  4304  from the water. When the right foot support  4301  is sliding rearward  4307 , the right paddle  4305  is rotated down into the water, so the sliding creates a forward  4309  thrust force against the water. 
       FIG. 43B  is a side view of a useful embodiment of another thrust assembly, where a foot holder  4310  is attached to a foot support  4311  that is connected to a thrust fin  4312 . The foot holder  4310  may be attached to the foot support  4311  using Velcro  4313 . Since the foot holder  4310  is attached near the toe portion  4314 , the rider is able to lift their heel  4315 , which is convenient when pushing the foot support rearward. In this thrust phase, when the foot holder  4310  slides the foot support  4311  rearward  4316 , the thrust fin  4312  also moves rearward  4317 , pushing against the water and generating forward thrust (i.e., to the right in the figure). The foot support  4311  is connected by a pinned rotary joint  4318  to a lever arm  4319  connected to the thrust fin  4312 , where the lever arm  4319  also comprises a rotary wheel  4320  to roll on the SUP  4321 . 
       FIG. 43C  is a side view of the useful embodiment of the thrust assembly of  FIG. 43B , where in this figure, the foot holder  4310  is pushing the foot support  4311  forward  4322 . The forward motion of the foot support  4311  causes the lever arm  4319  to rotate clockwise  4323  and rotate around the wheel  4320  and rotate the thrust fin  4312  out of the water. In this recovery phase, there is no water resistance applied to the thrust fin. 
       FIG. 43D  is a side view of a useful embodiment of another thrust assembly, where a foot holder  4324  is attached to a rotary foot support  4325  that is connected to a thrust fin  4326 . As shown, the foot holder  4324  is rotating the foot support  4325  clockwise  4327  about the rotary joint  4341  relative to the SUP  4328 . The rotation of the foot support  4325  causes the connecting rod  4329  to rotate the lever arm  4330  clockwise  4331  and rotate around the wheel  4332  and rotate the thrust fin  4326  out of the water  4340 . In this recovery phase, there is no water resistance applied to the thrust fin. 
       FIG. 43E  is a side view of the useful embodiment of the thrust assembly of  FIG. 43D . In this thrust phase, when the foot holder  4324  rotates the foot support  4325  counterclockwise  4333  about the rotary joint  4341  relative to the SUP  4328 , the thrust fin  4326  rotates into the water  4340  and moves rearward  4334 , pushing against the water and generating forward thrust (i.e., to the right in the figure). The foot support  4325  is connected by a connecting rod  4335  with pinned rotary joints  4336  and  4337  to a lever arm  4338  connected to the thrust fin  4326 , where the lever arm  4338  also comprises a rotary wheel  4339  to roll on the SUP  4328 . There is typically one foot holder for each foot, each with an associated foot support. The foot supports may be rotatably attached to a single SUP, or to two separate SUPs that may be propelled with forward/backward sliding motion by the rider, like Nordic snow skis, but floating and sliding on water. 
       FIG. 43F  is an end view of a useful embodiment of another thrust assembly, where rotary wheels  4342  roll on an SUP  4343 , the wheels  4342  are connected to a lever arm  4344  and to a thrust paddle  4345 , and where the thrust paddle  4345  is in the water  4346 . The outline for a foot holder  4347  provides where the rider&#39;s foot is typically positioned relative to the wheels  4342  and paddle  4345 . 
       FIG. 44  is a side view of a useful embodiment of another thrust assembly, where two four-bar linkages are used. The first four-bar linkage comprises links  4400 ,  4401 ,  4402 , and  4403 . The second four-bar linkage comprises links  4402 ,  4403 ,  4404 , and  4405 . The four-bar linkages are interconnected with rotary pinned joints. The first four-bar linkage positions the foot support  4406  relative to the SUP  4407 . The foot support  4406  is attached to the link  4403 . The second four-bar linkage positions the thrust fin  4408  relative to the position of the foot support  4406 . The thrust fin  4408  is attached to the link  4405 . As the foot support  4406  is rotated counterclockwise  4409  about the rotary pinned joint  4410 , the thrust fin  4408  is rotated clockwise about the rotary pinned joint  4412 . Accordingly, when the rider presses down with their foot  4413 , the thrust fin  4408  simultaneously moves down into the water and rearward  4411 , providing forward thrust. When the rider lifts their foot  4413 , the thrust fin  4408  retracts up. 
       FIG. 45A  is a side view of a useful embodiment of another thrust assembly, where two four-bar linkages are used. The first four-bar linkage comprises four revolute joints  4500  (grounded),  4501 ,  4502 , and  4503  (grounded). The second four-bar linkage comprises the four revolute joints  4503  (grounded),  4504 ,  4505 , and  4506  (grounded). Grounded revolute joints are affixed to an SUP; whereas, non-grounded revolute joints may translate relative to the SUP. Construction arcs  4507 ,  4508 ,  4509 , and  4510  are provided to indicate how the locations of the grounded revolute joints may be determined based on the desired starting and ending locations for the non-grounded revolute joints. From the starting location of the revolute joint  4504 , the construction arc  4507  is drawn with a radius equal to the length of the link  4511 ; from the ending location of the revolute joint  4504 ′, another construction arc  4508  is drawn using the same radius. The intersection of the two arcs  4507  and  4508  provides the location for the grounded revolute joint  4503 . From the starting location of the revolute joint  4505 , the construction arc  4509  is drawn with a radius equal to the length of the link  4512 ; from the ending location of the revolute joint  4505 ′, another construction arc  4510  is drawn using the same radius. The intersection of the two arcs  4509  and  4510  provides the location for the grounded revolute joint  4506 . 
     The rider places their foot  4513  on the foot support  4514  that is connected to the SUP by the grounded revolute joint  4500 . The rear of the foot support is connected to the lever arm  4515  of the crank link  4511  by a coupler  4516 . The foot support  4514  comprises a crank link, such that when the rider presses down on the foot support  4514  to rotate it counterclockwise  4542 , the coupler  4516  causes the lever arm  4515  of the crank link  4511  of the second four-bar linkage to rotate clockwise  4517 . The thrust fin  4518  comprises the coupling link of the second four-bar linkage between revolute joints  4504  and  4505 , where the thrust fin  4518  translates down  4521  into the water  4519  as it also rotates clockwise  4520  to a second position  4518 ′, and provides forward thrust to the SUP. 
       FIG. 45B  is a side view of a useful embodiment of another thrust assembly, similar to  FIG. 45A , but which adds a third four-bar linkage. The first four-bar linkage comprises four revolute joints  4522  (grounded),  4523 ,  4524 , and  4525  (grounded). The second four-bar linkage comprises the four revolute joints  4525  (grounded),  4526 ,  4527 , and  4528  (grounded). Grounded revolute joints are affixed to an SUP; whereas, non-grounded revolute joints may translate relative to the SUP. Construction arcs  4529 ,  4530 ,  4531 , and  4532  are provided to indicate how the locations of the grounded revolute joints may be determined based on the desired starting and ending locations for the non-grounded revolute joints. From the starting location of the revolute joint  4526 , the construction arc  4529  is drawn with a radius equal to the length of the link  4533 ; from the ending location of the revolute joint  4526 ′, another construction arc  4530  is drawn using the same radius. The intersection of the two arcs  4529  and  4530  provides the location for the grounded revolute joint  4525 . From the starting location of the revolute joint  4527 , the construction arc  4531  is drawn with a radius equal to the length of the link  4534 ; from the ending location of the revolute joint  4527 ′, another construction arc  4532  is drawn using the same radius. The intersection of the two arcs  4531  and  4532  provides the location for the grounded revolute joint  4528 . 
     The rider places their foot  4535  on the foot support  4536  that is connected to the SUP by the grounded revolute joint  4522 . The rear of the foot support is connected to the lever arm  4537  of the crank link  4533  by a coupler  4538 . The foot support  4536  comprises a crank link, such that when the rider presses down on the foot support  4536  to rotate it counterclockwise  4543 , the coupler  4538  causes the lever arm  4537  of the crank link  4533  of the second four-bar linkage to rotate clockwise  4539 . The coupling link  4540  of the second four-bar linkage rotates clockwise to a second position  4540 ′. 
     A third four-bar linkage comprises the four revolute joints  4528  (grounded),  4527 ,  4544 , and  4545  (grounded). A thrust fin  4546  is connected to the coupler  4548  between revolute joints  4527  and  4544 . When the coupler  4540  rotates clockwise (as did the thrust fin  4518  in  FIG. 45A ), it forces the crank link  4534  also to rotate clockwise. Since the crank link  4547  of the third four-bar linkage is the same length as the crank link  4534 , the coupler  4548  between the crank links  4534  and  4347  maintains its orientation relative to the SUP as it translates to its ending position  4548 ′. Likewise, the thrust fin  4546  which is connected to the coupler  4548  maintains its vertical orientation relative to the SUP as it translates  4549  through the water  4550  to its ending position  4546 ′, while providing forward thrust to the SUP. 
       FIG. 46A  is a side view of a useful embodiment of another thrust assembly, where a four-bar linkage is used comprising the four revolute joints  4600  (grounded),  4601  (grounded),  4602 , and  4603 . A thrust fin  4604  extends from the coupler  4605  between revolute joints  4602  and  4603 . The rider places their foot  4606  on the foot support  4607  that is connected to the SUP  4610  by the grounded revolute joint  4600 . The rear of the foot support is connected to the coupler  4605  by the revolute joint  4603 . The foot support  4607  comprises a crank link, where the rider presses down on the foot support  4607  to rotate it counterclockwise  4608 . Since the length between the revolute joints  4602  and  4603  is less than between the revolute joints  4600  and  4601 , downward movement of the coupler  4605  causes the thrust fin  4604  to rotate counterclockwise  4609  as it translates downward and to the left until it reaches its final position  4604 ′, generating forward thrust to the right as it translates. 
       FIG. 46B  is a side view of a useful embodiment of another thrust assembly, where a four-bar linkage is used similar to  FIG. 46A , but with additional links added. A four-bar linkage is used comprising the four revolute joints  4611  (grounded),  4612  (grounded),  4613 , and  4614 . A thrust fin  4615  extends from the coupler  4616  between revolute joints  4613  and  4614 . The rider places their foot  4617  on the foot support  4618  that is connected to the SUP  4621  by the grounded revolute joint  4611 . The rear of the foot support is connected to the coupler  4616  by the revolute joint  4614 . The foot support  4618  comprises a crank link, where the rider presses down on the foot support  4618  to rotate it counterclockwise  4619 . Since the length between the revolute joints  4613  and  4614  is less than between the revolute joints  4611  and  4612 , downward movement of the coupler  4616  causes it to rotate counterclockwise. The tie link  4621  connects the ground link  4622  to the lever arm  4623  extending from the thrust fin  4615 , causing the thrust fin  4615  to rotate clockwise  4620  more rapidly as it rotates to its final position  4615 ′ as the rider presses down on the foot support  4618 . 
       FIG. 47A  is a side view of a useful embodiment of another thrust assembly, where a four-bar linkage is used comprising the four revolute joints  4700  (grounded),  4701 ,  4702 , and  4703  (grounded). A thrust fin  4704  extends from the coupler  4705  between revolute joints  4701  and  4702 , and the rider places their foot  4706  on the foot support  4707  that is connected to the coupler  4705 . A revolute joint  4702  connects the rear portion of the coupler  4705  to the rear crank  4708  that is connected to the SUP  4709  by the grounded revolute joint  4703 . A revolute joint  4701  connects the front portion of the coupler  4705  to the front crank  4710  that is connected to the SUP  4709  by the grounded revolute joint  4700 . When the rider presses down on the foot support  4707 , it rotates clockwise. Since the length of the front crank  4710  is less than the length of the rear crank  4708 , downward movement of the coupler  4705  causes it to rotate clockwise, and the thrust fin  4704  to move down into the water and rearward to a second position  4704 ′, generating forward thrust. 
       FIG. 47B  is a rear end view of a useful embodiment of another thrust assembly, where left and right feet  4711  and  4712 , respectively are alternately pressing down on two foot supports  4713  and  4714 , respectively, each connected to a thrust fin  4715  and  4716 , respectively. The right foot support  4714  is elevated such that the connected thrust fin  4716  is above the water level  4717 , and not producing any resistance to forward travel of the SUP  4718 . The left foot support  4713  is pressed down such that the connected thrust fin  4715  is in the water and able to apply thrust. 
       FIG. 47C  is a side view of a useful embodiment of a thrust fin assembly, where the thrust fin  4718  is connected to a member  4719  by a revolute joint  4720 . The member comprises a detent  4721  to prevent the thrust fin  4718  from rotating counterclockwise (in the figure) past a limit orientation  4722  during the thrust phase  4723 , but where the thrust fin  4718  can rotate clockwise (in the figure)  4725  to a limit orientation  4724  when the member  4719  is not moving, or is moving against the water, so the thrust fin  4718  doesn&#39;t impede forward movement. This embodiment is useful when it is desired that a fin only generate forward thrust when moving in a rearward direction, but where the fin should minimize water drag when moving in a forward direction through the water. 
       FIG. 47D  is a side view of a useful embodiment of another thrust assembly, where a four-bar linkage is used comprising the four revolute joints  4726  (grounded),  4727 ,  4728 , and  4729  (grounded). A thrust fin  4730  extends from the coupler  4731  between revolute joints  4727  and  4728 , and the rider places their foot  4732  on the foot support  4733  that is connected to the front crank  4734  which is connected to the SUP  4735  by the grounded revolute joint  4726 . A revolute joint  4728  connects the coupler  4731  to the rear crank  4736  which is connected to the SUP  4735  by the grounded revolute joint  4729 . When the rider presses down  4737  on the foot support  4733 , it rotates counterclockwise, and the rear crank  4736  rotates clockwise  4738 , and the thrust fin  4730  moves down into the water  4739  and rearward  4740  to a second position  4730 ′, generating forward thrust. If the rider removes downward force from the foot support  4733  when the revolute joint  4728  is as far down as it can travel, momentum of the rear crank  4736  will move the thrust fin  4730  to a third position  4730 ″ out of the water, while simultaneously lifting the foot support  4733 . As the rider continues pumps the foot support  4733  up and down, the thrust fin  4730  will repeatedly enter the water  4739 , move rearward  4730 ′ to generate forward thrust, and then lift out of the water  4730 ″. 
       FIG. 47E  is a side view of a useful embodiment of a crank assembly for providing thrust. The crank assembly comprises a front crank  4741 , which may be substituted for the rear crank  4736  of  FIG. 47D . The present crank assembly comprises a four-bar linkage with four revolute joints  4742  (grounded),  4743 ,  4744 , and  4745  (grounded). The front crank  4741  comprises the link between the revolute joints  4742  and  4743 . A thrust fin  4746  is connected to a coupler  4747  between the revolute joints  4743  and  4744 . As provided in  FIG. 47D , typically a rider places their foot on a foot support (not shown in  FIG. 47E ) that is connected to the front crank  4741  (i.e., the rear crank  4736  in  FIG. 47D ) which is connected to the SUP  4748  by the grounded revolute joint  4742 . A revolute joint  4744  connects the coupler  4747  to the rear crank  4749  which is connected to the SUP  4748  by the grounded revolute joint  4745 . As shown in  FIG. 47D , when the rider presses down on the foot support, it rotates the front crank  4741  clockwise (i.e., the rear crank  4736  in  FIG. 47D ), and accordingly the thrust fin  4746  moves down into the water and rearward  4750  to a second position  4746 ′, generating forward thrust. The rear crank  4749  adjusts the angle of the thrust fin as it moves down into the water and rearward. 
       FIG. 47F  is a side view of a useful embodiment of a crank assembly for providing thrust. The crank assembly comprises a crank  4751 , which may be substituted for the rear crank  4736  of  FIG. 47D . The crank  4751  also functions like the member  4719  of  FIG. 47C , where the crank  4751  is connected to a thrust fin  4752 , and where the crank  4751  comprises a detent  4753 . The other end of the crank  4751  is connected by a grounded revolute joint  4754  to the SUP  4755 . The detent  4753  prevents the thrust fin  4752  from rotating counterclockwise around the revolute joint  4756  past a limit position, but where the thrust fin  4752  may rotate freely in a clockwise direction. The detent comprises a structure that limits a portion  4757  of the thrust fin  4752  from rotating past it. In this way, the thrust fin  4752  can apply forward thrust to the SUP  4755  while the crank  4751  is rotating clockwise and the thrust fin is moving to a second position  4758 , but the thrust fin  4752  applies minimal water drag when the crank  4751  stops rotating, or rotates counterclockwise. 
       FIG. 48A  is a side view of a useful embodiment of another thrust assembly, where a foot support  4800  may be pumped up and down  4801  to rotate a shaft  4802 , where the shaft  4802  may turn a propeller  4803 , or a paddle wheel, or other propulsion apparatus. In this figure, the shaft  4802  is mechanically connected to the shaft of the propeller  4803  using a torsion cable  4804  in a sheath  4805  that transmits rotary motion like a dentist drill cable. 
       FIG. 48B  is a plan view of the useful embodiment of  FIG. 48A . The torsion cable  4804  is connected  4806  to the shaft of the propeller  4803 . 
       FIG. 49A  is a side view of a useful embodiment of another thrust assembly, where one or more thrust fins rotate relative to foot supports. During a thrust phase where the rider uses their foot  4900  to press a foot support  4901  rearward  4910 , the thrust fins  4902  and  4903  rotate counterclockwise down into the water  4904  about revolute joints  4905  and  4906 , respectively, on the foot support  4901 , and press against detent/limit stops  4907  and  4908 , respectively, to resist the thrust fins  4902  and  4903  from rotating further counterclockwise. While pressing against the detent/limit stops  4907  and  4908 , the thrust fins may apply a thrust force against the water  4904  to move the SUP  4909  forward. The foot supports may use wheels  4912  and  4913  to slide along the surface of the SUP  4909 . 
       FIG. 49B  is a side view of the useful embodiment of  FIG. 49A  during a recovery phase, where the rider uses their foot  4900  to press the foot support  4901  forward  4911 . During the recovery phase, the thrust fins  4902  and  4903  rotate clockwise about revolute joints  4905  and  4906 , respectively, on the foot support  4901 , to slide along the top of the water  4904 , or out of the water, to minimize water resistance. 
       FIG. 49C  is a plan view of the useful embodiment of  FIGS. 49A and 49B , where the rider uses their foot  4900  to move the foot support  4901 . Thrust fins  4902  and  4903  are shown rotated relative to the foot support  4901 , to slide along the top of the water  4904 , or out of the water, to minimize water resistance. The foot support is shown with wheels  4912 ,  4913 ,  4914 , and  4915 , to slide along the surface of the SUP  4909 . Handlebars  4916  may be used to press against, and to steer the rudder  4917 . 
       FIG. 49D  is a plan view of a useful embodiment of another thrust assembly, where a thrust fin  4918  rotates relative to a foot support  4919 . During a thrust phase where the rider uses their foot  4920  to press the foot support  4919  rearward, the thrust fin  4918  rotates down into the water about a revolute joint on the foot support  4919  and applies a thrust force against the water to move the SUP  4921  forward. The foot support  4919  may use wheels  4922 ,  4923 ,  4924 , and  4925  to slide along the top of the SUP  4921 . The foot support  4919  may comprise a roller skates with wheels. The thrust fin  4918  may have roller wheels  4926  and  4927  to help slide along the top of the SUP  4921 , and may be connected by a connector  4928  to the foot support  4919 . The thrust fin  4918  may extend from the wheels  4926  and  4927  into the water to the side of the SUP  4921 . The SUP  4921  may have guard rails or a wall  4929  to help guide movement of the foot support  4919 . Movement of the foot support  4919  may be constrained with a linear bearing. Handlebars  4930  may be used to press against, and to steer the rudder  4931 . 
       FIG. 50A  is a side view of a useful embodiment of a foot holder  5000  and a foot support  5001 , where the foot holder  5000  comprises protrusions  5002  that mate with sockets  5003  on the foot support  5001 . The mating protrusions  5002  and sockets  5003  can transmit tangential force from the foot holder  5000  to the foot support  5001 , but yet the foot holder  5000  and foot support  5001  may be easily separated. The mating protrusions  5002  and sockets  5003  may lightly snap together or use Velcro. The foot support  5001  may comprise roller wheels  5004  and  5005 . 
       FIG. 50B  is a side view of a useful embodiment of the foot holder  5000  and a foot support  5001  of  FIG. 50A , where the wheels  5004  and  5005  are guide wheels constrained within a guide  5006 , which may operate like a garage-door wheel guide. The guide  5006  may be on top of the SUP  5007 , as provided in  FIG. 50B , or inset inside the SUP, as provided in  FIG. 50C . One guide wheel  5008  may support a thrust fin. Handlebars  5009  may be used to press against, to steer a rudder, to brake, or for balance. 
       FIG. 50C  is a side view of a useful embodiment of guide wheels  5010  and  5011  constrained within a guide  5012 , which may operate like a garage-door wheel guide. The guide  5012  may be inset inside the SUP  5013 . One guide wheel  5014  may support a thrust fin  5015 . 
       FIG. 50D  is a rear end view of a useful embodiment of guide wheels of  FIG. 50C , where the guide wheels are constrained within a guide  5012  inset inside the SUP  5013 . A foot holder  5016  is mated with a foot support  5017 . The guide wheels  5011  and  5018  are connected to the foot support  5017  with revolute joints  5019  and  5020 , respectively. When the guide  5012  is inset inside the SUP  5013 , the thrust fin  5015  is typically positioned beneath the foot support  5017 . 
       FIGS. 50E, 50F, and 50G  are a side views of a useful embodiment of a foot support, where a thrust fin is connected to the foot support by a connector. In operation, a typical thrust progression is from  FIG. 50G to 50E to 50F , but  FIG. 50E  will be described first here. In  FIG. 50E , a foot support  5021  comprises load-bearing wheels  5022  and  5023 , which may be guided by guides. The foot support  5021  may also comprise sockets  5024  for mating with protrusions of a foot support (such as shown in  FIG. 50A ). A thrust fin  5025  with a lever arm  5026 , which may be an “L” shaped lever arm, is connected by the lever arm  5026  to the foot support  5021  by a connector  5027 . The thrust fin  5025  is also connected to a roller wheel  5028  by a revolute joint  5029 , where the roller wheel  5028  is not directly connected to the foot support  5021 . The thrust fin  5025  may comprise a scoop  5030  for re-directing water  5031  when the thrust fin  5025  moves rearward  5032 . The scoop  5030  may also help apply a force from re-directed water  5031  to rotate the thrust fin counterclockwise to vertical, as well as translate the thrust fin  5025  forward relative to the foot support  5021 , since the scoop  5030  is positioned below the revolute joint  5029  of the roller wheel  5028 . 
       FIG. 50F  is a side view of a useful embodiment of the foot support of  FIG. 50E , where due to pressure from the water, the thrust fin  5025  has been rotated to vertical and translated forward relative to the foot support  5021  when the foot support is pushed rearward  5032  during the thrust phase by the rider. In this view, the roller wheel  5028 ′ is positioned farther to the right than the roller wheel  5028  shown in  FIG. 50E . 
       FIG. 50G  is a side view of a useful embodiment of the foot support of  FIG. 50E , where due to pressure from the water, the thrust fin  5025  has been rotated to nearly horizontal and translated rearward relative to the foot support  5021  when the foot support is pushed forward  5033  during the recovery phase by the rider. In this view, the roller wheel  5028 ″ is positioned farther to the left than the roller wheel  5028  shown in  FIG. 50E . 
       FIG. 50H  is a rear end view of a useful embodiment of the foot support of  FIGS. 50E, 50F, and 50G . A foot holder  5046  is mated with a foot support  5035 . There are typically a left  5034  and a right  5035  foot support which operate similarly, so only the right foot support  5035  will be describe here in detail. The foot support  5035  comprises load-bearing wheels  5036  and  5037 , which may be guided by guides  5038  and  5039 , respectively, connected to an SUP  5040 . A thrust fin  5041  with a lever arm  5042 , which may be an “L” shaped lever arm, is connected by the lever arm  5042  to the foot support  5035  by a connector  5043 . The thrust fin  5041  is also connected to a roller wheel by a revolute joint, where the roller wheel is not directly connected to the foot support  5035 . Handlebars  5044  may be used by the rider to press against, and to steer the rudder  5045 . 
       FIG. 50I  is a side view of a useful embodiment of a foot support  5046  similar to  FIG. 50E , but where the thrust fin  5047  is positioned to the rear of the foot support  5046 , rather than under or to the side of the foot support  5046 . 
       FIG. 50J  is a plan view of a useful embodiment of the foot support of  FIGS. 50E, 50F, 50G, and 50H . In  FIG. 50J , a foot support  5048  comprises load-bearing wheels  5049 ,  5050 ,  5051 , and  5052 , which may be guided by guides  5053  and  5054  connected to the SUP  5062 . The guides  5053  and  5054  may operate like garage-door guides for the garage-door wheels. The foot outline  5065  indicates where a rider typically stands on the foot support  5048 . A thrust fin  5055  with a lever arm  5056 , which may be an “L” shaped lever arm, is connected by the lever arm  5056  to the foot support  5048  by a connector  5057 . The thrust fin  5055  is also connected to a roller wheels  5058  and  5063  by a revolute joint  5059  to prevent the thrust fin  5055  from twisting (e.g., clockwise or counterclockwise in the plan view), where the roller wheels  5058  and  5063  are not directly connected to the foot support  5048 . There may be an axil support  5064  for the roller wheels  5058  and  5063 . Handlebars  5060  may be used by the rider to press against, and to steer the rudder  5061 . 
       FIG. 50K  is a plan view of a useful embodiment of the foot support of  FIG. 50J , where wheels  5065 ,  5066 ,  5067 , and  5068  with vertical axes (i.e., out of the paper) support torsional force (i.e., counterclockwise) from water pressure against the thrust fin  5069  during the thrust phase. The vertical-axis wheels  5065 ,  5066 ,  5067 , and  5068  are guided by wheel guides  5070  and  5071 . The vertical-axis wheels  5065 ,  5066 ,  5067 , and  5068  are connected by revolute joints to an axil support  5072 . The thrust fin  5069  may have roller wheels  5073  and  5074  that are also guided by the wheel guides  5070  and  5071 , respectively. The roller wheels  5073  and  5074  of the thrust fin  5069  may also be connected to the axil support  5072 . The thrust fin  5069  is shown with a lever arm  5075 , such as the lever arm described in detail in preceding figures, however additional features are omitted in this figure for clarity. 
       FIG. 50L  is a plan view of a useful embodiment of the foot support of  FIG. 50J , where wheels  5076  and  5077  with vertical axes (i.e., out of the paper) support torsional force (i.e., counterclockwise) from water pressure against the thrust fin  5078  during the thrust phase. While four vertical-axis wheels may be used as provided by  FIG. 50K , only two vertical-axis wheels are needed to resist the torsional force against the thrust fin  5078  during the thrust phase. The vertical-axis wheels  5076  and  5077  are guided by wheel guides  5079  and  5080 . The vertical-axis wheels  5076  and  5077  are connected by revolute joints to an axil support  5081 . Rider load-bearing wheels  5082 ,  5083 ,  5084 , and  5085  may also be connected to the axil support  5081 , and they are guided by the wheel guides  5079  and  5080 . The thrust fin  5078  may also be connected to the axil support  5081 . The thrust fin  5078  is shown with a lever arm  5086 , such as the lever arm described in detail in preceding figures, however additional features are omitted in this figure for clarity. 
       FIG. 51A  is a side view of a useful embodiment of a foot holder  5100  and a foot support  5101  guided by a linear bearing  5102  and a bearing rod  5103  on an SUP  5104 . The foot support  5101  may comprise support wheels  5105  and  5106 . Handlebars  5107  may be used to press against, to steer a rudder  5108 , to brake, or for balance. 
       FIGS. 51B, 51C, and 51D  are a side views of a useful embodiment of a foot support  5109 , where a thrust fin  5110  is connected to the foot support  5109  by a connector  5111 . In operation, a typical thrust progression is from  FIG. 51D  (the recovery phase) to  51 C to  51 B, but  FIG. 51B  will be described first here. In  FIG. 51B , a foot support  5109  comprises load-bearing wheels  5112  and  5113 , which may be guided by a linear bearing  5114  and bearing rod  5115  on an SUP  5116 . In  FIG. 51B , the linear bearing is associated with the front wheel  5112 . The thrust fin  5110  with a lever arm  5117 , which may be an “L” shaped lever arm, is connected by the lever arm  5117  to the foot support  5109  by the connector  5111 . The thrust fin  5110  is also connected to a roller wheel  5118  by a revolute joint  5119 , where the roller wheel  5118  is guided by a linear bearing  5123  and the bearing rod  5115 , and it is not directly connected to the foot support  5109 . The thrust fin  5110  may comprise a scoop  5120  for re-directing water when the thrust fin  5110  moves rearward  5121 . The scoop  5120  may also help apply a force from re-directed water to rotate the thrust fin counterclockwise to vertical, as well as translate the thrust fin  5110  forward relative to the foot support  5109 , since the scoop  5120  is positioned below the revolute joint  5119  of the roller wheel  5118 . 
       FIG. 51C  is a side view of a useful embodiment of the foot support of  FIG. 51B , where due to pressure from the water, the thrust fin  5110  has been rotated to nearly vertical and translated forward relative to the foot support  5109  when the foot support is pushed rearward during the thrust phase by the rider. In this view, the roller wheel  5118 ′ is positioned farther to the left than the roller wheel  5118  shown in  FIG. 51B . 
       FIG. 51D  is a side view of a useful embodiment of the foot support of  FIG. 51B , where due to pressure from the water, the thrust fin  5110  has been rotated to nearly horizontal and out of the water and translated rearward relative to the foot support  5109  when the foot support is pushed forward  5122  during the recovery phase by the rider. In this view, the roller wheel  5118 ″ is positioned farther to the left than the roller wheel  5118  shown in  FIG. 51B  and the roller wheel  5118 ′ in  FIG. 51C . 
       FIG. 51E  is a plan view of a useful embodiment of the foot support of  FIG. 51B , where the roller wheels  5118  and  5124  are guided by the linear bearing  5123  and the bearing rod  5115 . The thrust fin  5110  is connected to the revolute joint  5119  of the roller wheel  5118 . The thrust fin  5110  is shown with a lever arm  5117 , such as the lever arm described in detail in preceding figures, however additional features are omitted in this figure for clarity. 
       FIG. 51F  is a rear end view of a useful embodiment of the foot support of  FIG. 51B , where the roller wheels  5118  and  5124  are guided by the linear bearing  5123  and the bearing rod  5115 . The thrust fin  5110  is connected to the revolute joint  5119  of the roller wheel  5118 . The thrust fin  5110  is shown with a lever arm  5117 , such as the lever arm described in detail in preceding figures, however additional features are omitted in this figure for clarity. 
       FIG. 51G  is a side view of a useful embodiment of a foot holder  5125  and a foot support  5126  guided by a linear bearing  5127  and a bearing rod  5128  on an SUP  5129 . During the recovery phase, the rider is moving the foot support forward  5130 . The foot support  5126  may comprise support wheels  5131  and  5132 . The linear bearing  5127  may be associated with the front wheel  5131 . The thrust fin  5133  with a lever arm  5134 , which may be an “L” shaped lever arm, is connected by the lever arm  5134  to the foot support  5126  by the connector  5135 . The thrust fin  5133  is also connected to a roller wheel  5136  by a revolute joint  5137 , where the roller wheel  5136  is guided by the linear bearing  5139  and the bearing rod  5128 , and it is not directly connected to the foot support  5126 . During the recovery phase, the thrust fin  5133  is rotated clockwise from vertical by the connector  5135  pulling on the lever arm  5134 . The thrust fin  5133  may comprise a scoop  5138  for re-directing water when the thrust fin  5133  moves rearward during the thrust phase. The scoop  5138  may also help apply a force from re-directed water to rotate the thrust fin  5133  counterclockwise to vertical during the thrust phase, as well as translate the thrust fin  5133  forward relative to the foot support  5126 , since the scoop  5138  is positioned below the revolute joint  5137  of the roller wheel  5136 . 
       FIG. 51H  is a side view of the useful embodiment of  FIG. 51G  during the thrust phase. During the thrust phase, the rider typically lifts their heel  5140  and applies rearward  5141  force from the front portion  5142  of their foot, similar to how a Nordic snow skier propels themselves on Nordic snow skis. During the thrust phase, the rear wheel  5132  may lift off the SUP  5129 . During the thrust phase, the rider is moving the foot support rearward  5141 , and the thrust fin  5133  is rotated counterclockwise to vertical by the connector  5135  pushing on the lever arm  5134 . The scoop  5138  may also help apply a force from re-directed water to rotate the thrust fin  5133  counterclockwise to vertical during the thrust phase, as well as translate the thrust fin  5133  to the right relative to the foot support  5126 , since the scoop  5138  is positioned below the revolute joint  5137  of the roller wheel  5136 . 
       FIG. 51I  is a plan view of a useful embodiment of the foot support  5126  of  FIGS. 51G and 51H . The foot support is guided by the linear bearing  5127  and the bearing rod  5128  on an SUP. The linear bearing  5127  may be associated with the front support wheels  5131  and  5143 . The front support wheels  5131  and  5143  may swivel  5148  around the linear bearing  5127  by the revolute joint  5147 . 
       FIG. 51J  is a plan view of a useful embodiment of the foot support  5126  of  FIGS. 51G and 51H , where the foot support  5126  may comprise a roller skate shoe comprising the front support wheels  5131  and  5143  of  FIG. 51I . The foot support  5126  is outlined by a dashed line  5144 . The foot support  5126  is guided by the linear bearing  5127  and the bearing rod  5128  on an SUP. The foot support  5126  may also comprise the rear support wheels  5145  and  5146 . 
       FIG. 51K  is a plan view of a useful embodiment of the foot support  5126  of  FIG. 51J , where the foot support  5126  is swiveled clockwise about the revolute joint  5147 . The foot support  5126  is outlined by a dashed line  5144 . The foot support  5126  is guided by the linear bearing  5127  and the bearing rod  5128  on an SUP. The foot support  5126  may also comprise the rear support wheels  5145  and  5146 . 
       FIG. 52A  is a side view of a useful embodiment of a foot holder  5200  and a foot support  5201 , where the foot holder  5200  comprises a socket  5202  that mates  5206  with a protrusion  5203  on the foot support  5201 . The mating socket  5202  and protrusion  5203  can transmit tangential force  5207  from the foot holder  5200  to the foot support  5201 , but yet the foot holder  5200  and foot support  5201  may be easily separated. The mating socket  5202  and protrusion  5203  may lightly snap together or use cotton Velcro  5208  and hook Velcro  5209 . The foot support  5201  may comprise roller wheels  5204  and  5205  that roll on an SUP  5210 . 
       FIG. 52B  is a side view of a useful embodiment of a foot holder  5211  and a foot support  5212 , where the foot holder  5211  comprises a socket  5213  that mates with a protrusion  5214  on the foot support  5212 . The mating socket  5213  and protrusion  5214  can transmit tangential force from the foot holder  5211  to the foot support  5212 , but yet the foot holder  5211  and foot support  5212  may be easily separated. The mating socket  5213  and protrusion  5214  may lightly snap together or use additional mating snap components  5215  and  5216 , which may operate like blue jeans snaps, and are more secure than Velcro. The foot support  5212  may be connected by a connector  5217  to a linear bearing  5218  that rides on a bearing rod  5219  connected to an SUP  5220 . 
       FIG. 52C  is a side view of a useful embodiment of the foot holder  5211  and the foot support  5212  of  FIG. 52B , where the mating snap components  5215  and  5216  provide sufficient tangential support so that the socket  5213  and protrusion  5214  of  FIG. 52B  aren&#39;t needed. 
       FIG. 52D  is a side view of a useful embodiment of a foot holder  5221  and a foot support  5222 , where the foot holder  5221  comprises a clasp  5223  with a return spring  5224  that mates with a pin  5225  on the foot support  5222 . The front of the clasp  5223  may be curved  5226  to slide over the pin  5225  on the foot support  5222  when the front end  5227  of the foot holder  5221  slides forward  5228  under the pin  5225 . The clasp  5223  and pin  5225  can transmit tangential force from the foot holder  5221  to the foot support  5222 , but yet the foot holder  5221  and foot support  5222  may be easily separated by pressing down on the clasp lever  5229  to rotate it counterclockwise  5230  against the return force of the return spring  5224 . The foot support  5222  may comprise roller wheels  5231  and  5232  that roll on an SUP  5233 . 
       FIG. 52E  is a side view of a useful embodiment of the foot holder  5221  and the foot support  5222  of  FIG. 52D , where the front end  5227  of the foot holder  5221  has slid forward under the pin  5225  of the foot support  5222 , securing the foot holder  5221  to the foot support  5222 . 
       FIGS. 52F-520  provide useful embodiments of various thrust assemblies and components where a thrust fin automatically rotates into the water to provide thrust against the water during the thrust phase where the rider translates their foot rearward relative to an SUP, and the thrust fin automatically rotates out of the water to minimize drag during the recovery phase where the rider translates their foot forward relative to the SUP. 
       FIG. 52F  is a perspective view of a useful embodiment of another thrust assembly, where a foot support  5233  is connected to a thrust fin  5234  by a connector  5235 . The foot support may be guided by a linear bearing  5236  with bearing rod  5244  attached to a moveable support  5237 . The thrust fin  5234  is connected by a lead-screw bearing  5238  to a lead screw  5239  (or a worm screw, or a cork screw threaded rod) that is also attached to the moveable support  5237 . When the foot support  5233  moves forward  5245  relative to the moveable support  5237 , the connector  5235  pulls the thrust fin  5234  forward  5241 , causing the thrust fin  5234  to rotate clockwise  5240  about the lead screw  5239  and rise out of the water as it translates forward  5241  relative to the moveable support  5237 . The entire moveable support may move on a linear bearing  5242  and may translate relative to the SUP  5243 . 
       FIG. 52G  is a perspective view of a useful embodiment of another thrust assembly similar to  FIG. 52F , but where the thrust fin  5246  not only rises up  5247  as it is pulled forward by a connector  5248 , but it also rotates clockwise  5249  about its own axis to quickly remove drag of the thrust fin  5246  during the recovery phase. 
       FIG. 52H  is a perspective view of a useful embodiment of another thrust assembly, where a foot support  5250  is connected to a thrust fin  5251  by a connector  5252  and a set of beveled gears, which may be right-angled gears or spiraled gears. The foot support  5250  may be guided by a linear bearing  5253  with bearing rod  5254  attached to a moveable support  5255 . The connector  5252  connects the foot support  5250  to a lever arm  5256  that turns a first bevel gear  5257 . The first bevel gear  5257  meshes with a second bevel gear  5258  that is connected to the thrust fin  5251 . When the foot support  5250  moves forward  5259  relative to the moveable support  5255 , the connector  5252  pulls  5264  the lever arm  5256  forward  5260 , causing the bevel gears  5257  and  5258  to rotate  5261  the thrust fin  5251  out of the water. The entire moveable support  5255  may move on a linear bearing  5262  and may translate relative to the SUP  5263 . The shaft of the thrust fin may comprise a counterweight  5264 . 
       FIG. 52I  is a perspective view of a useful embodiment of another thrust assembly, where a foot support  5265  is connected to a thrust fin  5266  by a rack  5267  and pinion gear  5268  connected to a set of beveled gears, which may be right-angled gears or spiraled gears. The foot support  5265  may be guided by a linear bearing  5269  with bearing rod  5270  attached to a moveable support  5271 . When the foot support  5265  translates forward  5272  relative to the moveable support  5265 , it translates the rack  5267  past the pinion gear  5268  which turns a first bevel gear  5273 . The first bevel gear  5273  meshes with a second bevel gear  5274  that is connected to the thrust fin  5266 , where the bevel gears  5273  and  5274  rotate  5275  the thrust fin  5266  out of the water. The entire moveable support  5271  may move on a linear bearing  5276  and may translate relative to the SUP  5277 . The shaft of the thrust fin  5266  may comprise a spring  5278  to offset weight of the thrust fin  5266 . 
       FIG. 52J  is a perspective view of a useful embodiment of another thrust assembly, where a foot support  5279  is connected to a thrust fin  5280  by a tendon  5281 , which may be wire rope, which passes around and rotates a pair of pulleys that may be at an angle to each other. The foot support  5279  may be attached to a bearing rod  5283  that is guided by linear bearings  5282  and  5292  that are attached to a moveable support  5284 . When the foot support  5279  translates forward  5293  relative to the moveable support  5284 , it translates  5294  the bearing rod  5283 , which translates  5295  the tendon  5281  past the first pulley  5285  which turns  5296  the first pulley  5285 . The tendon then passes over a second pulley  5286  that is connected to the thrust fin  5280 , where rotation  5297  of the second pulley  5286  rotates  5287  the thrust fin  5280  out of the water. The entire moveable support  5284  may translate on a linear bearing  5288  relative to the SUP  5289 . In the figure, the tendon  5281  is shown to start from a point  5290  on the foot support  5279 , then pass over the top of the first pulley  5285 , then pass under the second pulley  5286  and wrap around to the top, and then pass under the first pulley  5285 , and exit over the top of the first pulley  5285  where it connects to the bearing rod  5283  at a point  5291 . However, any suitable path around the pulleys  5285  and  5286  for the tendon  5281  will suffice. 
       FIG. 52K  is a perspective view of a useful embodiment of another thrust assembly that is similar to the thrust assembly of  FIG. 52J , but which uses three tendon pulleys to route the tendon and raise/lower a thrust fin. A foot support  5298  is connected to a thrust fin  5299  by a tendon  5200 A, which may be wire rope, which passes around and rotates a set of pulleys. The foot support  5298  may be attached to a bearing rod  5201 A that is guided by linear bearings  5202 A and  5203 A that are attached to a moveable support  5204 A. When the foot support  5298  translates forward  5205 A relative to the moveable support  5204 A, it translates  5206 A the bearing rod  5201 A, which translates  5207 A the tendon  5200 A past the first pulley  5208 A which turns the first pulley  5208 A. The tendon  5200 A then passes around a second pulley  5209 A that is connected to the thrust fin  5299 , where rotation of the second pulley  5209 A rotates  5210 A the thrust fin  5299  out of the water. The tendon then passes around a third pulley  5211 A and is attached to the bearing rod  5201 A. The entire moveable support  5204 A may translate on a linear bearing  5212 A relative to the SUP  5213 A. In the figure, the tendon  5200 A is shown to start from a point  5214 A on the foot support  5298 , then pass behind the first pulley  5208 A, then pass 1.5 times around the second pulley  5209 A exiting from the bottom, and then pass around the right of the third pulley  5211 A, and exit from the rear left of the third pulley  5211 A where it then connects to the bearing rod  5201 A at a point  5215 A. However, any suitable path around the pulleys  5208 A,  5209 A, and  5211 A for the tendon  5200 A will suffice. 
       FIG. 52L  is a perspective view of a useful embodiment of another thrust assembly which comprises a microprocessor, an accelerometer, a battery, computer memory, a computer program, and a motor  5216 A. A foot support  5217 A may be guided by a linear bearing  5218 A with bearing rod  5219 A attached to an SUP  5220 A. When forward acceleration of the foot support  5217 A is sensed, the motor lifts the thrust fin  5221 A from the water and rotates it, and when rearward acceleration of the foot support is sensed, the motor rotates the thrust fin and lowers it into the water. 
       FIG. 52M  is a perspective view of a useful embodiment of another thrust assembly which comprises a module  5222 A comprising a microprocessor, an accelerometer, a battery, computer memory, a computer program, and a motor. A foot support  5223 A may be guided by a linear bearing  5224 A with bearing rod  5225 A attached to an SUP  5226 A. A moveable gear  5227 A is attached to the thrust fin  5228 A and meshes with a stationary gear  5229 A which may be attached to the module  5222 A. When forward acceleration of the foot support  5223 A is sensed, the motor moves the moveable gear  5227 A relative to the stationary gear  5229 A, and the thrust fin  5228 A simultaneously rises  5230 A from the water and rotates  5231 A about its own axis. When rearward acceleration of the foot support  5223 A is sensed, the motor moves the moveable gear  5227 A in the opposite direction relative to the stationary gear  5229 A, and the thrust fin  5228 A simultaneously lowers into the water and rotates about its own axis. 
       FIG. 52N  is an end view of the useful embodiment of  FIG. 52M  which comprises a module  5222 A comprising a microprocessor, an accelerometer, a battery, computer memory, a computer program, and a motor. The moveable gear  5227 A is attached to the thrust fin  5228 A and meshes with a stationary gear  5229 A which may be attached to the module  5222 A. When forward acceleration of the foot support is sensed, the motor moves the moveable gear  5227 A counterclockwise  5232 A relative to the stationary gear  5229 A, and the thrust fin  5228 A simultaneously rises  5230 A from the water and rotates  5231 A about its own axis. When rearward acceleration of the foot support is sensed, the motor moves the moveable gear  5227 A in the opposite direction relative to the stationary gear  5229 A, and the thrust fin  5228 A simultaneously lowers into the water and rotates about its own axis. 
       FIG. 52O  is a side view of a useful embodiment of a thrust fin assembly comprising a detent  5233 A for holding a thrust fin  5234 A in a desired orientation. A detent support  5235 A comprises the detent  5233 A with return spring  5236 A. The thrust fin  5234 A comprises a catch  5237 A that when the thrust fin  5234 A is rotated  5238 A, the catch  5237 A depresses the detent  5233 A. When the catch  5237 A passes past the detent  5233 A and moves to a second position  5237 A′, the return spring  5236 A un-depresses the detent  5233 A. The catch  5237 A then rests against the detent  5233 A, and prevents the thrust fin  5234 A from rotating back to its original orientation until the catch  5237 A is released by depressing the detent  5233 A. 
       FIG. 53A  is a rear end view of a useful embodiment of another thrust assembly, where a foot holder  5300  is mated with a foot support  5301 . There are typically a left and a right foot support which operate similarly, so only the right foot support  5301  will be describe here. The foot support  5301  comprises at least a load-bearing wheel  5302 , which may be guided by the guide  5303  connected to an SUP  5304 . The guide  5303  may be a track or rail. A thrust fin  5305  is connected to a roller wheel or the foot support  5301  by a revolute joint  5306 . The foot support  5301  also comprises guide wheels  5307  and  5308  with vertical axes, which may be guided by the guide  5303 . Foam  5309 , such as neoprene, may be placed around the guide  5303  and other apparatus to protect the rider in the case they fall. 
       FIG. 53B  is a side view of a useful embodiment of another thrust assembly, where a foot holder  5310  is mated with a foot support  5311 . The foot support  5311  comprises the load-bearing wheels  5312  and  5313 , which may be guided by the guide  5314  connected to an SUP  5315 . The guide  5314  may comprise a track or rail. The foot support  5311  also comprises guide wheels  5316  and  5317  with vertical axes, which may be guided by the guide  5314 . 
       FIG. 53C  is a plan view of a useful embodiment of another thrust assembly, where a foot  5318  rests on a foot support  5319 , each indicated with dashed outlines. The foot support  5319  comprises the load-bearing wheels  5320 ,  5321 ,  5322 , and  5323 . The foot support  5319  also comprises the guide wheels  5324 ,  5325 ,  5326 , and  5327  with vertical axes, which may be guided by the guide  5328  connected to an SUP  5329 . The guide  5328  may comprise a track or rail. A thrust fin  5330  may be connected to a roller wheel  5331 , a load-bearing wheel  5320 , or the foot support  5319 . 
       FIG. 53D  is a side view of a useful embodiment of another thrust assembly, where a foot holder  5332  rests on a foot support  5333 . The foot support  5333  comprises the load-bearing wheels  5334  and  5335 . The foot support  5333  also comprises the guide wheels  5336  and  5337 , where guide wheel  5336  comprises a vertical axis. The guide wheels  5336  and  5337  may be guided by the guide  5338  connected to an SUP  5339 . The guide  5338  may comprise a track or rail. 
       FIG. 53E  is a side view of a useful embodiment of a portion of a thrust assembly guided by a linear bearing  5340  and a bearing rod  5341  connected to an SUP  5342 . The linear bearing  5340  may be connected to a wheel  5343 . 
       FIG. 53F  is a plan view of a useful embodiment of a portion of a thrust assembly guided by a linear bearing  5344  and a bearing rod  5345  on an SUP  5346 . The linear bearing  5344  may be connected to the wheels  5347  and  5348 . The wheels  5347  and  5348  may swivel around the linear bearing  5344  by the revolute joint  5349 , and may comprise a return spring  5350 . The return sprint  5350  encourages the wheels  5347  and  5348  to remain centered, but allows them to rotate about the revolute joint  5349  if twisted by the rider to assist with turning the SUP  5346 . A thrust fin  5351  may be connected to the axil of a wheel, such as the wheel  5347 , or to the linear bearing  5344 . 
       FIG. 53G  is a rear end view of a useful embodiment of another thrust assembly, where a foot holder  5352  is mated with a foot support  5353 . The foot support  5353  comprises the load-bearing wheels  5354  and  5355 . The foot support  5353  also comprises the guide wheels  5356  and  5357  with horizontal axes, and comprises the guide wheels  5358  and  5359  with vertical axes. The guide wheels  5356 ,  5357 ,  5378 , and  5359  may be guided by the guide  5360  connected to an SUP  5361 . The guide  5360  may comprise a track or rail. 
       FIG. 53H  is a rear end view of a useful embodiment of another thrust assembly, where a foot holder  5362  is mated with a foot support  5363 . The foot support  5363  comprises the load-bearing wheels  5364  and  5365 . The foot support  5363  also comprises the linear bearing  5366 . The load bearing  5366  may be guided by the bearing rod  5367  connected to an SUP  5368 . 
       FIG. 53I  is a side view of a useful embodiment of a thrust fin assembly comprising a detent  5369  for holding a thrust fin  5370  in a desired orientation, such as rotated up out of the water. When the thrust fin  5370  is rotated from a first position  5371  to a second position  5372 , it depresses the detent  5369  which rotates (into the page as shown) about the detent axis  5373 . The thrust fin  5370  then passes past the detent  5369  and moves to the second position  5372  and is supported there by the detent  5369  that has un-depressed. The detent  5369  prevents the thrust fin  5370  from rotating back to its original first position  5371  until the thrust fin  5370  is released from the detent  5369  by depressing the detent  5369 . 
       FIG. 53J  is a side view of a useful embodiment of the thrust fin assembly of  FIG. 53I  comprising the detent  5369  for holding the thrust fin  5370  in a desired orientation, such as rotated up out of the water. When the thrust fin  5370  is rotated from a first position  5371  to a second position, it depresses the detent  5369  which rotates (counterclockwise as shown to the dashed position  5374 ) about the detent axis  5373 . The thrust fin  5370  then passes past the detent  5369  and moves to the second position and is supported there by the detent  5369  that has un-depressed. The detent  5369  prevents the thrust fin  5370  from rotating back to its original first position  5371  until the thrust fin  5370  is released from the detent  5369  by depressing the detent  5369 . 
       FIG. 53K  is a side view of a useful embodiment of a thrust fin assembly comprising a detent  5375  for holding a thrust fin  5376  in a desired orientation, such as rotated up out of the water. When the thrust fin  5376  is rotated from a first position to a second position  5377 , the cam  5378  that is attached to the thrust fin  5376  depresses the detent  5375  which rotates (into the page as shown) about the detent axis  5379 . The thrust fin  5376  then passes past the detent  5375  and moves to the second position  5377  and is supported there by a flat  5380  on the cam  5378  resting against the detent  5375  that has un-depressed. The detent  5375  prevents the thrust fin  5376  from rotating back to its original first position until the thrust fin  5376  is released from the detent  5375  by depressing the detent  5375 . 
       FIG. 53L  is a side view of a useful embodiment of the thrust fin assembly of  FIG. 53K  comprising the detent  5375  for holding the thrust fin  5376  in a desired orientation, such as rotated up out of the water. When the thrust fin  5376  is rotated from a first position  5381  to a second position, the cam  5378  that is attached to the thrust fin  5376  depresses the detent  5375  which rotates (counterclockwise as shown to the dashed position  5382 ) about the detent axis  5379 . The thrust fin  5376  then passes past the detent  5375  and moves to the second position and is supported there by a flat on the cam  5378  resting against the detent  5375  that has un-depressed. The detent  5375  prevents the thrust fin  5376  from rotating back to its original first position until the thrust fin  5376  is released from the detent  5375  by depressing the detent  5375 . 
       FIG. 53M  is a plan view of a useful embodiment of another thrust assembly which may comprise any of the useful embodiments of  FIGS. 53A-53L , where thrust fins  5383  and  5384  rotate relative to foot supports  5385  and  5386  guided by linear bearings with bearing rods  5387  and  5388 . Outlines  5389  and  5390  show where a rider typically places their feet on the foot supports  5385  and  5386 . The width  5391  of the placement of the bearing rods  5387  and  5388  on the SUP  5392  may be adjusted by the rider. The foot supports  5385  and  5386  may be compatible with Nordic (a.k.a. cross-country) snow ski bindings and shoes. 
       FIG. 54A  is a perspective view of a useful embodiment of another thrust assembly, where a foot support  5400  is connected to a thrust fin  5401  by a connector  5402  and a set of meshing gears, which may be spiraled gears. The foot support  5400  may be guided by a linear bearing  5403  with bearing rod  5404  attached to a moveable support  5405 . The connector  5402  connects the foot support  5400  to a lever arm  5406  that turns a first gear  5407 . The first gear  5407  meshes with a second gear  5408  that is connected to the thrust fin  5401 . When the foot support  5400  moves forward  5409  relative to the moveable support  5405 , the connector  5402  pulls the lever arm  5406  clockwise  5410 , causing the meshing gears  5407  and  5408  to rotate  5411  the thrust fin  5401  out of the water. The entire moveable support  5405  may move on a linear bearing  5412  and may translate relative to the SUP  5413 . In operation, when the first gear  5047  rotates 90 degrees, the thrust fin  5401  may rotate up 45 degrees. 
       FIG. 54B  is a perspective view of a useful embodiment of a thrust fin assembly comprising a detent for holding a thrust fin  5414  in a desired orientation, such as rotated out of the water. The detent comprises a plunger  5415  in the fin arm  5416 , which may include a cylinder or ball, and comprises an opening  5417  in a retaining sleeve  5418  into which the plunger may extend and lodge. The fin arm  5416  comprises a cavity comprising the plunger  5415  that is pressed by a spring  5419  to extend outward from an opening  5420  in the fin arm  5416 . The fin arm  5416  is inserted  5421  into the retaining sleeve  5418 . The retaining sleeve  5418  may be attached to a foot support, such as the foot support  5400  in  FIG. 54A , or may be attached to an apparatus connected to the foot support  5400 , such as the second gear  5408  in  FIG. 54A . When the thrust fin  5414  is rotated from a first position  5422  to a second position, the plunger  5415  is pressed against the inside of the retaining sleeve  5418  by the spring  5419  as it slides along the inside of the retainer sleeve  5418  until the plunger  5415  extends and lodges into the opening  5417  in the receiver sleeve  5418 , and holds the fin arm  5416  in an orientation relative to the retainer sleeve  5418 . The detent prevents the thrust fin  5414  from rotating back to its original first position  5422  until the fin arm  5416  is released from the detent by depressing the plunger  5415 . 
       FIG. 54C  is a perspective view of the useful embodiment of the thrust fin assembly of  FIG. 54B  comprising a detent for holding the thrust fin  5414  in a desired orientation. When the thrust fin  5414  is rotated from a first position to a second position  5423 , the plunger  5415  is pressed against the inside wall  5424  of the retaining sleeve  5418  by the spring  5419  as it slides along the inside wall  5424  of the retainer sleeve  5418  until the plunger  5415  extends and lodges into the opening  5417  in the receiver sleeve  5418 , and holds the fin arm  5416  in an orientation relative to the retainer sleeve  5418 . The detent prevents the thrust fin  5414  from rotating back to its original first position until the fin arm  5416  is released from the detent by depressing the plunger  5415 . 
       FIG. 54D  is a side view of a useful embodiment of another thrust assembly comprising spring-loaded one-way flaps  5425  and associated stationary inclined surfaces  5426 . The inclined surfaces  5426  are attached to an SUP  5427 , and the flaps  5425  are rotationally attached to the inclined surfaces by revolute joints  5428  and comprise return springs  5429 . A thrust paddle arm  5430  of a thrust paddle  5431  is typically connected directly or by other apparatus to a foot support (not shown) such that movement of the foot support by the SUP rider translates the thrust paddle  5431 . Below, postfixes A, B, C, and D are used to represent the thrust paddle arm  5430  at different locations. The flaps only allow the thrust paddle arm  5430  of the thrust paddle  5431  to translate rearward (i.e., to the left in the figure)  5432  through the flaps  5425 , and they don&#39;t permit the thrust paddle arm  5430  to return forward (i.e., to the right in the figure) through the flaps  5425 . That is, the flaps  5425  will rotate clockwise (in the figure) about their revolute joints  5428  against the force of the springs  5429  when the thrust paddle arm  5430 A presses against them from the right side in the figure. When a thrust paddle arm  5430 B is translated forward relative to the SUP  5427 , the flaps  5425  remain pressed down against the SUP  5427 , and they redirect the thrust paddle arm  5430 C up along 5433 one of the inclined surfaces  5426  in order to raise the thrust paddle  5431  out of the water. After passing over the peak edge  5434  of an inclined surface  5426 , the thrust paddle arm  5430 D will then drop back down to the surface of the SUP  5427 . Multiple flaps  5425  with inclined surfaces  5426  may be used simultaneously, so when the thrust paddle  5431  is at almost any location along the SUP  5427 , if it is translated forward, there is a flap  5425  and inclined surface  5426  nearby to direct the thrust paddle arm  5430  up. 
       FIG. 54E  is a side view of a useful embodiment of the thrust assembly of  FIG. 54D  comprising a spring-loaded one-way flap  5435  and associated stationary inclined surface  5436 . The inclined surface  5436  is attached to an SUP  5437 , and the flap  5435  is rotationally attached to the inclined surface by a revolute joint  5438  and comprises a return spring  5439 . A thrust paddle arm  5440  of a thrust paddle  5441  is typically connected directly or by other apparatus to a foot support (not shown) such that movement of the foot support by the SUP rider translates the thrust paddle  5441 . The flap only allow the thrust paddle arm  5440  of the thrust paddle  5441  to translate rearward (i.e., to the left in the figure) through the flap  5435 , and the flap  5435  doesn&#39;t permit the thrust paddle arm  5440  to return forward (i.e., to the right in the figure) through the flap  5435 . That is, the flap  5435  will rotate clockwise (in the figure) about its revolute joint  5438  against the force of the spring  5439  when the thrust paddle arm  5440  presses against it from the right side in the figure. 
       FIG. 54F  is a side view of the useful embodiment of the thrust assembly of  FIG. 54E  comprising a spring-loaded one-way flap  5435  and associated stationary inclined surface  5436 . In this figure, the thrust paddle arm  5440  with thrust paddle  5441  is shown passing rearward (i.e., to the left in the figure) underneath the flap  5435  while compressing the spring  5439  as the flap  5435  is rotated counterclockwise by the thrust paddle arm  5440 . 
       FIG. 54G  is a side view of a useful embodiment of another thrust assembly, where a thrust paddle  5442  for an SUP  5443  is stable in either of two positions. The thrust paddle  5442  is attached to a foot support  5444  by a revolute joint  5445 . The foot support  5444  comprises a first  5446  and a second  5447  limit stop. The foot support  5444  also comprises a spring  5448 , where the spring  5448  is attached to the foot support  5444  at a first location  5449 , and is attached to the thrust paddle  5442  at a second location  5450 . Due to the tension in the spring  5448 , the thrust paddle  5442  will only be stable when resting against the first  5446  or the second  5447  limit stop. In this figure, the thrust paddle  5442  is provided resting stably against the first  5446  limit stop, where the thrust paddle  5442  is out of the water  5451 . 
       FIG. 54H  is a side view of the useful embodiment of the thrust assembly of  FIG. 54G , where the thrust paddle  5442  for the SUP  5443  is stable in either of two positions. In this figure, the thrust paddle  5442  is provided resting stably against the second  5447  limit stop, where the thrust paddle  5442  is in the water  5451 . 
       FIG. 54I  is a side view of a useful embodiment of another thrust assembly, where a thrust paddle  5452  for an SUP  5453  is stable in either of two positions. The thrust paddle  5452  is attached to a foot support  5454  by a paddle revolute joint  5455 . The foot support  5454  comprises a first  5456  and a second  5457  limit stop. The foot support  5454  also comprises a spring  5458 , where the spring  5458  is attached to the foot support  5454  at a first location  5459 , and is attached to the thrust paddle  5452  at a second location  5460 . Due to the tension in the spring  5458 , the thrust paddle  5452  will only be stable when resting against the first  5456  or the second  5457  limit stop. In this figure, the thrust paddle  5452  is provided resting stably against the first  5456  limit stop, where the thrust paddle  5452  is out of the water  5461 . An optional foot holder  5462  is shown mated with the foot support  5454 . The foot support  5454  is shown to be supported on the SUP  5453  by a linear bearing assembly similar to  FIG. 53H . Here, the foot support  5454  comprises the load-bearing wheels  5463  and  5464 . The foot support  5454  also comprises the linear bearing  5465 . The linear bearing  5465  may be guided by the bearing rod  5466  connected to the SUP  5453 . The arm of the thrust paddle  5452  extends  5467  and comprises a roller  5468  on the end opposite to the thrust paddle  5452 . The roller  5468  rolls through paths in a guide  5469  that comprises a set of constraints to move the roller up and down and, in effect, to determine whether the thrust paddle  5452  is in the water  5461  or out of the water  5461 . 
       FIG. 54J  is a side view of the useful embodiment the constraint guide  5469  of  FIG. 54I . The constraint guide  5469  comprises an upper path  5480  and a lower path  5481 , where the two paths are separated by one-way spring-loaded flaps  5470  and  5471 . The first flap  5470  can rotate counterclockwise around a revolute joint  5472  while pushing against a return spring  5473 . The first flap  5470  cannot rotate clockwise from the shown position. Similarly, the second flap  5471  can rotate counterclockwise around a revolute joint  5474  while pushing against a return spring  5475 . The second flap  5471  cannot rotate clockwise from the shown position. The arm of the thrust paddle  5452  comprises a roller  5468  (shown with a dashed circle in locations indicated by  5468 A, B, C, and D) on the end opposite to the thrust paddle  5452  (in  FIG. 54I ). The roller  5468  passes through paths in a guide  5469  that comprises a set of constraints to move the roller up and down and, in effect, to determine whether the thrust paddle  5452  (in  FIG. 54I ) is in the water  5461  or out of the water  5461 . When the foot support  5454  (in  FIG. 54I ) is forward relative to the SUP  5453 , the roller  5468 A is positioned in the upper right of the constraint guide  5469 , where the thrust paddle  5452  is in the water  5461 . As the rider pushes the foot support  5454  rearward the roller also moves rearward  5476  to the roller location  5468 B, and forward thrust is provided to the SUP  5453 . As the rider continues to push the foot support  5454  rearward, the roller also moves rearward  5477 , and the roller passes past the first one-way spring-loaded flap  5470  to reach the roller location  5468 C in the lower left of the constraint guide  5469 , where the thrust paddle  5452  is raised above the water  5461  as the roller reaches the roller location  5468 C. As the rider pushes the foot support  5454  forward, the roller also moves forward  5478  to the roller location  5468 D, and there is no resistance from the water since the thrust paddle  5452  is still out of the water  5461 . As the rider continues to push the foot support  5454  forward, the roller also moves forward  5479 , and the roller passes past the second one-way spring-loaded flap  5471  to reach the roller location  5468 A in the upper right of the constraint guide  5469  where the cycle started, and where the thrust paddle  5452  is lowered into the water  5461  as the roller reaches the roller location  5468 D. The thrust paddle  5452  also may rotate rearward (i.e., clockwise) to prevent drag while the SUP  5453  is gliding or while the thrust paddle  5452  is being pushed forward, and may use the thrust fin assembly of  FIGS. 54B and 54C  comprising a detent. 
       FIG. 55A  is a rear end view of a useful embodiment of another thrust assembly, where a thrust paddle  5500  for an SUP  5501  is stable in either of two positions. The thrust paddle  5500  is attached to a foot support  5502  by a paddle revolute joint  5503 . The foot support  5502  comprises a first  5504  and a second  5505  limit stop. The foot support  5502  also comprises a spring  5506 , where the spring  5506  is attached to the foot support  5502  at a first location  5507 , and is attached to the thrust paddle  5500  at a second location  5508 . Due to the tension in the spring  5506 , the thrust paddle  5500  will only be stable when resting against the first  5504  or the second  5505  limit stop. In this figure, the thrust paddle  5500  is provided resting stably against the first  5504  limit stop, where the thrust paddle  5500  is out of the water  5509 . An optional foot holder  5510  is shown mated with the foot support  5502 . The foot support  5502  is shown to be supported on the SUP  5501  by a linear bearing assembly similar to  FIG. 53H . Here, the foot support  5502  comprises the load-bearing wheels  5511  and  5512 . The foot support  5502  also comprises the linear bearing  5513 . The linear bearing  5513  may be guided by the bearing rod  5514  connected to the SUP  5501 . The arm of the thrust paddle  5500  extends  5515  and comprises a roller  5516  on the end opposite to the thrust paddle  5500 . The roller  5516  rolls through paths in a guide  5517  that comprises a set of constraints to move the roller  5516  up and down and, in effect, to determine whether the thrust paddle  5500  is in the water  5509  or out of the water  5509 . 
     The thrust paddle arm  5518  of the thrust paddle  5500  comprises a lever arm  5519  and an axial revolute joint  5520 . When the foot support  5502  is moved forward on the SUP  5501 , the roller  5516  rotates the thrust paddle arm  5518  clockwise (in the figure) about the paddle revolute joint  5503 , and the thrust paddle  5500  is lowered into the water  5509  in an orientation about its axial revolute joint  5520  to apply forward thrust to the SUP  5501 . While providing forward thrust, the thrust paddle  5500  is prevented from rotating forward about the axial revolute joint  5520  by a thrust limit stop, but the thrust paddle  5500  may freely rotate rearward about the axial revolute joint  5520  to prevent water drag when the SUP  5501  is gliding and the thrust paddle  5500  is in the water  5509 . If the SUP  5501  is gliding, the thrust paddle  5500  rotates rearward about the axial revolute joint  5520  due to water  5509  pressing against it. When the thrust paddle  5500  is in this rearward rotated position, if the foot support  5502  is moved forward such that the roller  5516  causes the thrust paddle arm  5518  to rise, the lever arm  5519  contacts the upper portion  5521  of the first limit stop  5504 , causing the thrust paddle  5500  to rotate about its axial revolute joint  5520  to a vertical orientation, which positions the thrust paddle  5500  to apply forward thrust to the SUP  5501  when it is next lowered into the water  5509 . 
       FIG. 55B  is a side view of the useful embodiment of the thrust assembly of  FIG. 55A . The thrust paddle arm  5518  in a first position  5518 A of the thrust paddle  5500  in a first position  5500 A comprises a lever arm  5519  in a first position  5519 A and an axial revolute joint. When the foot support  5502  is moved forward (i.e., to the right in the figure) on the SUP  5501 , the roller rotates the thrust paddle arm  5518 A about the paddle revolute joint, and the thrust paddle  5500 A is lowered into the water  5509  in a vertical orientation about its axial revolute joint  5520  to apply forward thrust to the SUP  5501 . While providing forward thrust, the thrust paddle  5500  is prevented from rotating forward (counterclockwise in the figure) about the axial revolute joint  5520  by a thrust limit stop  5522 , but the thrust paddle  5500  may freely rotate rearward (clockwise in the figure) about the axial revolute joint to prevent water drag when the SUP  5501  is gliding and the thrust paddle  5500  is in the water  5509 . If the SUP  5501  is gliding, the thrust paddle  5500  rotates rearward (clockwise in the figure) to position  5500 B about the axial revolute joint due to water  5509  pressing against it. When the thrust paddle  5500 B is in this rearward rotated position, if the foot support  5502  is moved forward such that the roller  5516  causes the thrust paddle arm  5518 B to rise, the lever arm  5519 B contacts the upper portion  5521  of the first limit stop  5504 , causing the thrust paddle  5500 B to rotate (counterclockwise in the figure) about its axial revolute joint  5520  to a vertical orientation, which positions the thrust paddle  5500 A to apply forward thrust to the SUP  5501  when it is next lowered into the water  5509 . 
       FIG. 55C  is a side view of a useful embodiment of the constraint guide  5517  of  FIG. 55A . In the current figure,  FIG. 55C , the constraint guide  5523  comprises an upper path  5524  and a lower path  5525 , where the two paths are separated by one-way spring-loaded flaps  5526 ,  5527 , and  5528 . Three flaps are shown, however, there may by any number of flaps depending on the length of the constraint guide  5523 . The flaps  5526 ,  5527 , and  5528  can rotate counterclockwise around the revolute joints  5529 ,  5530 , and  5531 , respectively, while pushing against the return springs  5532 ,  5533 , and  5534 , respectively. The flaps  5526 ,  5527 , and  5528  cannot rotate clockwise from the shown positions; however, the flaps  5526 ,  5527 , and  5528  can rotate counterclockwise around their respective revolute joints  5529 ,  5530 , and  5531  while pushing against their respective return springs  5532 ,  5533 , and  5534 . 
     In  FIG. 55A , the extension of the thrust paddle  5515  comprises the roller  5516  on the end opposite to the thrust paddle  5500 . In the current figure,  FIG. 55C , the roller  5516  is shown with a dashed circle in locations indicated by  5516 A, B, C, D, E, F, and G. The roller  5516  passes through the paths  5524  and  5525  in the guide  5523 , that comprises a set of constraints, to move the roller  5516  up and down and, in effect, to determine whether the thrust paddle  5500  (in  FIG. 55A ) is in the water or out of the water. When the foot support  5502  (in  FIG. 55A ) is forward relative to the SUP and the foot support  5502  is just starting to be pushed rearward by the rider, the roller  5516  in this figure,  FIG. 55C , is positioned at  5516 A in the upper right of the constraint guide  5523 , where the thrust paddle  5500  is in the water. As the rider pushes the foot support  5502  rearward, the roller  5516 A also moves rearward  5535 , and the roller  5516 A passes past the first one-way spring-loaded flap  5526  to reach the roller location  5516 B, while forward thrust is provided to the SUP  5536 . As the rider continues to push the foot support  5502  rearward  5539 , the roller  5516 B passes past the second one-way spring-loaded flap  5527  to reach the roller location  5516 C. As the rider continues to push the foot support  5502  as far rearward as possible, the roller  5516 C passes past  5540  the third one-way spring-loaded flap  5528  to reach the roller location  5516 D in the left of the constraint guide  5523 , where the thrust paddle  5500  is still in the water. 
     As the rider pushes the foot support  5502  forward, the roller  5516 D rolls down  5541  along the left side of the third flap  5528  which raises the thrust paddle  5500  out of the water, and the roller  5516 D also moves forward to the roller location  5516 E. There is no resistance from the water while the thrust paddle  5500  is out of the water. As the rider continues to push the foot support  5502  forward, the roller also moves forward  5537 , and the roller  5516 E passes past the second one-way spring-loaded flap  5527  to reach the roller location  5516 F. As the rider continues to push the foot support  5502  forward, the roller  5516 F also moves forward  5538 , and the roller  5516 F passes past the first one-way spring-loaded flap  5526  to reach the farthest-right roller location  5516 G in the lower right of the constraint guide  5523 . When the rider starts to push the foot support  5502  rearward to initiate the thrust phase again, the roller  5516 G rolls up  5542  the right side of the first flap  5526  to reach roller location  5516 A, where the cycle started, and where the thrust paddle  5500  is again lowered into the water. 
     While the foot support  5502  is moving rearward (to the left) in the upper path  5524  during the thrust phase, where the thrust paddle is in the water, at any time the foot support  5502  may be moved forward to initiate a recovery phase, and the roller  5516  will roll down the left side of the nearest flap to its right, and the thrust paddle  5500  will be raised from the water. While the foot support  5502  is moving forward (to the right) in the lower path  5525  during the recovery phase where the thrust paddle  5500  is out of the water, at any time the foot support  5502  may be moved rearward to initiate a thrust phase, and the roller  5516  will roll up the right side of the nearest flap to its left, and the thrust paddle  5500  will be lowered into the water. 
       FIG. 55D  is a side view of a useful embodiment of the constraint guide  5517  of  FIG. 55A . In the current figure,  FIG. 55D , the constraint guide  5543  comprises an upper path  5544  and a lower path  5545 , where the two paths are separated by one-way spring-loaded flaps  5546 ,  5547 ,  5548 ,  5549 ,  5550 ,  5551 ,  5552 , and  5553 . Four upper flaps and four lower flaps are shown, however, there may by any number of flaps depending on the length of the constraint guide  5543 . Each upper flap  5546 ,  5547 ,  5548 , and  5549  is paired with a lower flap  5550 ,  5551 ,  5552 , and  5553 , where the upper  5546 ,  5547 ,  5548 , and  5549  and lower  5550 ,  5551 ,  5552 , and  5553  flaps are separated by the stationary horizontal guides  5554 ,  5555 ,  5556 , and  5557 , respectively. The flaps  5546 ,  5547 ,  5548 ,  5549 ,  5550 ,  5551 ,  5552 , and  5553  can rotate counterclockwise around the revolute joints  5558 ,  5559 ,  5560 ,  5561 ,  5562 ,  5563 ,  5564  and  5565 , respectively, while pushing against the return springs  5566 ,  5567 ,  5568 ,  5569 ,  5570 ,  5571 ,  5572  and  5573 , respectively. The flaps  5546 ,  5547 ,  5548 ,  5549 ,  5550 ,  5551 ,  5552 , and  5553  cannot rotate clockwise from the shown positions; however, they can rotate counterclockwise around their respective revolute joints  5558 ,  5559 ,  5560 ,  5561 ,  5562 ,  5563 ,  5564  and  5565  while pushing against their respective return springs  5566 ,  5567 ,  5568 ,  5569 ,  5570 ,  5571 ,  5572  and  5573 . 
     In  FIG. 55A , the extension of the thrust paddle  5515  comprises the roller  5516  on the end opposite to the thrust paddle  5500 . In the current figure,  FIG. 55D , the roller  5516  is shown with a dashed circle in locations indicated by  5516 H, I, J, K, L, M, N, O, and P. The roller  5516  passes through the paths  5544  and  5545  in the guide  5543 , that comprises a set of constraints, to move the roller  5516  up and down and, in effect, to determine whether the thrust paddle  5500  (in  FIG. 55A ) is in the water or out of the water. When the foot support  5502  (in  FIG. 55A ) is forward relative to the SUP and the foot support  5502  is just starting to be pushed rearward by the rider, the roller  5516  in this figure,  FIG. 55D , is positioned at  5516 H in the upper right of the constraint guide  5543 , where the thrust paddle  5500  is in the water. As the rider pushes the foot support  5502  rearward (to the left), the roller  5516 H also moves rearward  5574 , and the roller  5516 H passes past the first one-way spring-loaded flap  5546  to reach the roller location  5516 I, while forward thrust is provided to the SUP  5575 . As the rider continues to push the foot support  5502  rearward  5576 , the roller  5516 I passes past the second one-way spring-loaded flap  5547  to reach the roller location  5516 J. As the rider continues to push the foot support  5502  rearward  5577 , the roller  5516 J passes past the third one-way spring-loaded flap  5548  to reach the roller location  5516 K. As the rider continues to push the foot support  5502  as far rearward as possible, the roller  5516 K passes past  5578  the fourth one-way spring-loaded flap  5549  to reach the roller location  5516 L in the left of the constraint guide  5543 , where the thrust paddle  5500  (in  FIG. 55A ) is still in the water, but starting to rise up. 
     As the rider pushes the foot support  5502  forward, the roller  5516 L rolls down  5579  along the left side of the fourth flap  5549  to the left side of the fifth flap  5550 , which raises the thrust paddle  5500  out of the water, and the roller  5516 L also moves forward to the roller location  5516 M. There is no resistance from the water while the thrust paddle  5500  is out of the water. As the rider continues to push the foot support  5502  forward, the roller  5516 M also moves forward  5580 , and the roller  5516 M passes past the sixth one-way spring-loaded flap  5551  to reach the roller location  5516 N. As the rider continues to push the foot support  5502  forward, the roller  5516 N also moves forward  5581 , and the roller  5516 N passes past the seventh one-way spring-loaded flap  5552  to reach the roller location  5516 O. As the rider continues to push the foot support  5502  forward, the roller  5516 O also moves forward  5582 , and the roller  5516 O passes past the eight one-way spring-loaded flap  5553  to reach the farthest-right roller location  5516 P in the right of the constraint guide  5543 , where the thrust paddle  5500  (in  FIG. 55A ) starts to lower. When the rider starts to push the foot support  5502  rearward to initiate the thrust phase again, the roller  5516 P rolls up  5583  the right side of the seventh flap  5553  to the right side of the first flap  5546  to reach roller location  5516 H, where the cycle started, and where the thrust paddle  5500  is again lowered into the water. 
     While the foot support  5502  is moving rearward (to the left) in the upper path  5544  during the thrust phase, where the thrust paddle is in the water, at any time the foot support  5502  may be moved forward to initiate a recovery phase, and the roller  5516  will roll down the left side of the nearest flap to its right, and the thrust paddle  5500  (in  FIG. 55A ) will be raised from the water. While the foot support  5502  is moving forward (to the right) in the lower path  5545  during the recovery phase where the thrust paddle  5500  (in  FIG. 55A ) is out of the water, at any time the foot support  5502  may be moved rearward to initiate a thrust phase, and the roller  5516  will roll up the right side of the nearest flap to its left, and the thrust paddle  5500  will be lowered into the water. 
       FIG. 56A  is a combined side/perspective view of a useful embodiment of another thrust assembly, where a rider  5600  is standing with their feet  5601  and  5602  on translatable foot supports  5603  and  5604 , and with their hands  5605  and  5606  on handlebars  5607  (shown using a perspective view) of an SUP  5608 . The foot support  5603  comprises a thrust paddle  5609  (shown using a perspective view) for applying thrust to the SUP  5608 . The handlebars  5607  comprise a joint  5610  for adjusting the handlebar position. 
       FIG. 56B  is a combined side/perspective view of a useful embodiment of another thrust assembly, where a rider  5611  is seated on a seat  5612  with a foot  5613  contacting a translatable foot support  5614 , and their hands  5615  and  5616  on handlebars  5617  (shown using a perspective view) of an SUP  5618 . The foot support  5614  comprises an inclined portion  5619  convenient for a seated position, where the inclined portion  5619  may tilt up, and the foot support  5614  further comprises a thrust paddle  5620  (shown using a perspective view) for applying thrust to the SUP  5618 . The handlebars  5617  comprise a joint  5621 , which may comprise a hinge, for adjusting the handlebar position to accommodate the seated position. The embodiment of  FIG. 56A  may easily convert into the embodiment of  FIG. 56B , and vice versa. 
       FIG. 57A  is a combined side/perspective view of a useful embodiment of another thrust assembly of an SUP  5700 , where a rider may stand with a foot  5701  on a translatable foot support  5702 , and place their hand on a hand lever  5704 . The foot support  5702  may slide relative to the SUP  5700 . The foot support  5702  comprises a thrust paddle  5705  (shown using a perspective view) that can rotate out of the water or into  5706  the water for applying thrust to the SUP  5700 . The hand lever  5704  comprises a revolute joint  5707  for rotating the hand lever forward  5708  and rearward. The hand lever  5704  controls the thrust paddle  5705 , and may comprise a linkage or a Bowden cable. In this figure, the hand lever  5704  is connected to the thrust paddle  5705  by a Bowden cable  5709 , with a first end  5710  of the tendon attached to the hand lever  5704 , and a second end  5711  attached to a rotary cam  5712  attached to the shaft  5713  of the thrust paddle  5705 . During the thrust phase, when the rider pushes rearward with their foot  5701  on the foot support  5702 , they simultaneously push their hand forward against the hand lever  5704 . When the hand lever  5704  moves forward  5708 , the tendon of the Bowden cable  5709  rotates the cam  5712  and causes the thrust paddle  5705  to rotate into  5706  the water. During the recovery phase, when the rider pushes forward with their foot  5701  on the foot support  5702 , they simultaneously pull their hand rearward against the hand lever  5704 . When the hand lever  5704  moves rearward, the tendon of the Bowden cable  5709  rotates the cam  5712  and causes the thrust paddle  5705  to rotate out of the water so it does not provide any resistance against the water. 
       FIG. 57B  is a combined side/perspective view of a useful embodiment of another thrust assembly for an SUP  5714 , where a rider may stand with a foot  5715  on a translatable foot support  5716 , and place their hand on a handle  5717  comprising a lever  5718 , similar to a bicycle brake lever. The foot support  5716  may slide relative to the SUP  5714 . The foot support  5716  comprises a thrust paddle  5719  (shown using a perspective view) that can rotate out  5720  of the water or into the water for applying thrust to the SUP  5714 . The lever  5718  controls the thrust paddle  5719 , and may comprise a linkage or a Bowden cable. In this figure, the lever  5718  is connected to the thrust paddle  5719  by a Bowden cable  5703 , with the first end  5721  of the tendon attached to the lever  5718 , and the second end  5722  attached to a rotary cam  5723  attached to the shaft  5724  of the thrust paddle  5719 . During the recovery phase, when the rider pushes forward with their foot on the foot support  5716 , they simultaneously squeeze their hand and pull their fingers rearward  5725  against the lever  5718 . When the lever  5718  is squeezed, the tendon of the Bowden cable  5703  rotates the cam  5723  and causes the thrust paddle  5719  to rotate out  5720  of the water so it does not provide any resistance against the water. During the thrust phase, when the rider pushes rearward with their foot on the foot support  5716 , they simultaneously open their hand and release their fingers from the lever  5718 . When the lever  5718  is released, the tendon of the Bowden cable  5703  rotates the cam  5723  and causes the thrust paddle  5719  to rotate into the water. 
       FIG. 58  is a perspective view of a useful embodiment of another thrust assembly for an SUP  5800  comprising translatable foot supports  5801  and  5802 . The foot supports  5801  and  5802  are shown in  FIG. 58  to slide on bearing rods  5803  and  5804 . Each foot support is connected to a paddle by a connector, and is capable of raising a paddle blade out of the water  5812 , or lowering the paddle blade into the water  5812 . The paddle may comprise a single handle  5805  with paddle blades  5806  and  5807  on opposite ends. The right foot support  5801  is connected by the right connector  5808  to the right portion  5809  of the paddle handle  5805 ; the left foot support  5802  is connected by the left connector  5810  to the left portion  5811  of the paddle handle  5805 . When a foot support moves forward, such as the right foot support  5801 , the right connector  5808  of the right foot support  5801  lifts the paddle blade  5806  over the water  5812  so there is no water resistance from the right paddle blade  5806 . When a foot support moves rearward, such as the left foot support  5802 , the left connector  5810  of the left foot support  5802  lowers the paddle blade  5807  into the water  5812  so the left paddle blade  5807  may apply thrust to the SUP  5800 . 
       FIG. 59A  is a side view of a useful embodiment of another thrust assembly for an SUP  5900  comprising a translatable foot support  5901 . The foot support  5901  is connected to a connecting joint  5902  which is connected to a paddle handle  5903 . The connecting joint  5902  is also connected by a connector  5904  to a linear bearing  5905  that slides on a bearing rod  5906 . The foot support  5901  is able to raise a paddle blade  5907  of the paddle handle  5903  out of the water, or lower the paddle blade  5907  into the water. The paddle handle  5903  may comprise paddle blades  5907  and  5908  on opposite ends. When the foot support  5901  lifts, the connecting joint  5902  lifts the right paddle blade  5908  over the water so there is no water resistance from the right paddle blade  5908 . When the foot support  5901  moves forward, the connecting joint  5902  pulls the linear bearing  5905  forward along the bearing rod  5906 . When the foot support  5901  moves rearward, the connecting joint  5902  lowers the paddle blade  5908  into the water so the paddle blade  5908  may apply thrust to the SUP  5900 . When the foot support  5901  moves rearward with the paddle blade  5908  in the water, the connecting joint  5902  pushes the linear bearing  5905  rearward along the bearing rod  5906  to propel the SUP  5900  forward. 
       FIG. 59B  is a plan view of the useful embodiment of the thrust assembly of  FIG. 59A  for the SUP  5900  comprising right and left translatable foot supports  5901  and  5909  connected to connecting joints  5902  and  5910 , respectively, which are each connected to the paddle handle  5903 . The connecting joints  5902  and  5910  are also connected by connectors  5904  and  5911  to linear bearings  5905  and  5912 , respectively, which slide on bearing rods  5906  and  5913 , respectively. The foot supports  5901  and  5909  are able to raise paddle blades  5907  and  5908  of the paddle handle  5903  out of the water, or lower the paddle blades  5907  and  5908  into the water. 
     When the right foot support  5901  lifts, the connecting joint  5902  lifts the right paddle blade  5907  over the water so there is no water resistance from the right paddle blade  5907 . When the foot support  5901  moves forward, the connecting joint  5902  pulls the connector  5904  to pull the linear bearing  5905  forward along the bearing rod  5906 . When the foot support  5901  moves rearward, the connecting joint  5902  lowers the paddle blade  5907  into the water so the paddle blade  5907  may apply thrust to the SUP  5900 . When the foot support  5901  moves rearward with the paddle blade  5907  in the water, the connecting joint  5902  pushes the connector  5904  to push the linear bearing  5905  rearward along the bearing rod  5906  to propel the SUP  5900  forward. 
     Similarly, when the left foot support  5909  lifts, the connecting joint  5910  lifts the left paddle blade  5908  over the water so there is no water resistance from the left paddle blade  5908 . When the foot support  5909  moves forward, the connecting joint  5910  pulls the connector  5911  to pull the linear bearing  5912  forward along the bearing rod  5913 . When the foot support  5909  moves rearward, the connecting joint  5910  lowers the paddle blade  5908  into the water so the paddle blade  5908  may apply thrust to the SUP  5900 . When the foot support  5909  moves rearward with the paddle blade  5908  in the water, the connecting joint  5910  pushes the connector  5911  to push the linear bearing  5912  rearward along the bearing rod  5913  to propel the SUP  5900  forward. 
       FIG. 60  is a plan view of another useful embodiment of a thrust assembly similar to  FIG. 59B , but where there are two separate paddle handles  6000  and  6001 , instead of one paddle handle with a paddle blade on each end. Each paddle handle  6000  and  6001  has a paddle blade  6002  and  6003  at one end, and an elevation/rotary joint  6004  and  6005  at the other end, respectively. Each of the elevation/rotary joints  6004  and  6005  comprises and elevation axis  6006  and  6007  about which the paddle handles  6000  and  6001  may elevate, respectively. The elevation axes  6006  and  6007  may have supports  6008  and  6009  for the axes  6006  and  6007  connected to rotary bases  6010  and  6011  that rotate about vertical (out of the page) axes  6012  and  6013 , respectively. The SUP  6014  comprises right and left translatable foot supports  6015  and  6016  connected to connecting joints  6017  and  6018 , respectively, which are connected to paddle handles  6000  and  6001 , respectively. The connecting joints  6017  and  6018  are also connected by connectors  6019  and  6020  to linear bearings  6021  and  6022 , respectively, which slide on bearing rods  6023  and  6024 , respectively. The foot supports  6015  and  6016  are able to raise the paddle blades  6002  and  6003  out of the water, or lower the paddle blades  6002  and  6003  into the water. 
     When a foot support, such as the right foot support  6015  lifts, the connecting joint  6017  lifts the right paddle blade  6002  over the water so there is no water resistance from the right paddle blade  6002 . When the foot support  6015  moves forward, the connecting joint  6017  pulls the connector  6019  to pull the linear bearing  6021  forward along the bearing rod  6023 . When the foot support  6015  moves rearward, the connecting joint  6017  lowers the paddle blade  6002  into the water so the paddle blade  6002  may apply thrust to the SUP  6014 . When the foot support  6015  moves rearward with the paddle blade  6002  in the water, the connecting joint  6017  pushes the connector  6019  to push the linear bearing  6021  rearward along the bearing rod  6023  to propel the SUP  6014  forward  6025 . Unlike the embodiment of  FIG. 59B , since the connecting joints  6017  and  6018  are connected to the paddle handles  6000  and  6001  away from their vertical axes of rotation  6012  and  6013 , respectively, when foot supports  6015  and  6016  move, the amounts of their movements are amplified to provide greater amounts of movement at the end of their respective paddle blades  6002  and  6003 . 
       FIG. 61A  is a plan view of another useful embodiment of a thrust assembly, where right and left foot supports  6100  and  6101  are connected by joints  6102  and  6103  to right and left connectors  6104  and  6105 , respectively, which are connected by joints  6106  and  6107  to right and left paddle handles  6108  and  6109 , respectively, where the paddle handles  6108  and  6109  have paddle blades  6110  and  6111  on one end and elevation/rotary joints  6112  and  6113 , respectively, connected to the SUP  6114  at the other end. Located on the SUP  6114  between the elevation/rotary joints  6112  and  6113  and the paddle blades  6110  and  6111  are handle guides  6115  and  6116  similar to the handle guide assembly provided by  FIG. 61B  (see  FIG. 61B  for details). As the foot supports  6100  and  6101  move forward and rearward relative to the SUP  6114 , the handle guides  6115  and  6116  lift the paddle blades  6110  and  6111  out of the water during the forward recovery phase, and guide the paddle blades  6110  and  6111  into the water during the rearward thrust phase. 
       FIG. 61B  is a side view of the embodiment of a handle guide assembly. A foot support is connected by joints to a paddle handle with a paddle blade, such as provided by  FIG. 61A . At the beginning of a paddle recovery phase, the foot support is in a rearward location relative to an SUP  6118 , where the paddle handle is in a first position  6119 , and the corresponding paddle blade is in the water. As rider moves their foot forward, the foot support starts moving forward, and the paddle handle is guided up  6120  to the top of a guide structure  6121  to a second position  6122 , where the paddle blade is guided out of the water. As the foot support continues forward, the paddle handle passes a top flap. The top flap is shown in a first top flap position  6123 , where the top flap has a top return spring  6124  pressing it against a top limit stop  6125 . As the paddle handle reaches the tip  6126  of the top flap, the top flap rotates temporarily to a second top flap position  6127 . Once the paddle handle passes the tip  6126  of the top flap, the rider of the SUP pulls their foot rearward to pull the foot support rearward. Once the foot support moves rearward, the attached paddle handle that is past the tip  6126  of the top flap moves  6117  to a third position  6128 , and the top return spring  6124  rotates the top flap back to the first top flap position  6123 . Once the paddle handle passes the tip  6126  of the top flap, when the foot support moves rearward, it can only move to the third position  6128 , since the top flap has returned to the first top flap position  6123 , preventing the paddle handle from returning to the second position  6122 . 
     As rider continues to pull the foot support rearward, the paddle arm moves along the bottom  6129  of the guide structure  6121  to a fourth position  6130 , where the paddle blade is guided into the water. As the rider continues to pull the foot support rearward, the paddle handle passes a bottom flap. The bottom flap is shown in a first bottom flap position  6131 , where the bottom flap has a bottom return spring  6132  pressing it against a bottom limit stop  6133 . As the paddle handle reaches the tip  6134  of the bottom flap  6131 , the bottom flap rotates temporarily to a second bottom flap position  6135 . Once the paddle handle passes the tip  6134  of the bottom flap, the rider of the SUP  6118  pushes their foot forward to push the foot support forward. Once the foot support moves forward, the attached paddle handle that is past the tip  6134  of the bottom flap and moves  6136  to the first position  6119 , and the bottom return spring  6132  rotates the bottom flap back to the first bottom flap position  6131 . Once the paddle handle passes the tip  6134  of the bottom flap, when the foot support moves forward, it can only move to the first position  6119 , since the bottom flap has returned to the first bottom flap position  6131 , preventing the paddle handle from returning to the fourth position  6130 . The cycle of the paddle handle being guided around the guide structure  6121  may repeat. 
       FIG. 61C  is a plan view of another useful embodiment of a thrust assembly, where a foot support  6137  is connected by joints  6138  and  6139  to right and left connectors  6140  and  6141 , respectively, which are connected by joints  6142  and  6143  to right and left paddle handles  6144  and  6145 , respectively, where the paddle handles  6144  and  6145  have paddle blades  6146  and  6147  on one end and elevation/rotary joints  6148  and  6149 , respectively, connected to the SUP  6150  at the other end. Accordingly, the single foot support  6137  may move both paddle blades  6146  and  6147 . The foot support connected to both paddle handles may be a right  6137  or a left  6151  foot support, or both. 
       FIG. 61D  is a plan view of another useful embodiment of a thrust assembly, where a foot support  6152  is connected by a joint  6153  to a multi-bar linkage  6154  (such as provided by  FIGS. 45-47 ) grounded  6155  to the SUP  6156  and connected to a paddle handle  6157 , where the paddle handle  6157  has a paddle blade  6158 . The linkage  6154  determines the position of the paddle blade  6158  based on the position of the foot support  6152 . 
       FIG. 62A  is a side view of another useful embodiment of a thrust assembly comprising a right  6200  and left flotation device for the right  6201  and left feet, respectively, of a rider  6202 . Only the right flotation device  6200  is provided in this figure. The rider  6202  may stand on a foot support  6203  on the flotation device  6200 . Each flotation device, such as the right flotation device  6200 , comprises one or more fins  6204  which may be extended into the water by the rider  6202  to provide “traction” during a thrust phase, or retracted during a recovery phase. During the recovery phase, the rider  6202  retracts the fins  6204  so the associated flotation device  6200  may glide along the surface of the water. In typical operation, the rider may pull rearward  6205  on a right handle  6206  that controls the fins  6204  of the right flotation device  6200  to extend  6207  them into the water to hold the right flotation device relatively stationary at that location in the water (see also  FIG. 62B ). The rider simultaneously pushes forward on the left handle that retracts the fins of the left flotation device from the water. While the rider pushes the left handle forward, they also push their left foot forward relative to their right foot  6201 , causing the left flotation device to glide forward on the water, since the left flotation device has its fins retracted, while the right flotation device  6200  doesn&#39;t move much since its fins are extended. The handle  6206  may be connected to the fins  6204  by a lever  6208  that rotates about a revolute joint  6209 , where counterclockwise rotation of the lever extends the fins  6204  into the water, and clockwise rotation of the lever  6204  retracts the fins from the water. 
       FIG. 62B  is a side view of the useful embodiment of the thrust assembly of  FIG. 62A , where the rider  6202  already pulled rearward on the right handle  6206  that controls the fins  6204  of the right flotation device  6200  to extend them into the water to hold the right flotation device  6200  relatively stationary at that location in the water. 
     The drawings and descriptions provided are intended to illustrate a variety of important elements of the invention, including components, assemblies, sub-assemblies, features, and the like. The elements provided are not intended to be limited only to the drawing in which they are shown. For clarity of the drawings, and so only a finite set of drawings are needed to exemplify the various elements of the invention, elements are included in some drawings and not in others to illustrate the different elements; however, the invention includes that elements in the drawings may be interchanged and or combined with elements in other drawings. For instance, the steering assembly in one drawing may be combined with the rudder assembly of another drawing, which may be combined with a braking assembly of another drawing, which may be combined with a paddle assembly from another drawing, which may be combined with the mechanical or electrical control from another drawing, and the like. Input controls may mechanically or electrically control output movement. Furthermore, the assemblies may be for attaching to an SUP at the factory, or the assemblies may be for attachment to a generic SUP already owned by the rider, i.e., retrofit. When paddle blades are used to provide thrust, a paddle blade may provide thrust by moving along the side of the SUP, moving under the SUP, moving through one or more openings in the SUP, or a combination. 
     All publications and patent applications cited in this specification are herein incorporated by reference as if each individual publication or patent application were specifically and individually indicated to be incorporated by reference. 
     Although the foregoing invention has been described in some detail by way of illustration and example for purposes of clarity of understanding, it will be readily apparent to those of ordinary skill in the art in light of the teachings of this invention that certain changes and modifications may be made thereto without departing from the spirit or scope of the appended claims.