Abstract:
A levitating platform, which is capable of stable flight, is disclosed. Levitating platform ( 100 ) comprises a platform structure ( 110 ), which includes a bottom extended surface ( 116 ) and a lip ( 114 ). An air movement device ( 120 ) is mounted on platform structure ( 110 ) to flow air ( 30 ) into plenum ( 123 ) between support surface ( 20 ), bottom extended surface ( 116 ) and lip ( 114 ). The flow of air ( 30 ) in plenum ( 123 ) creates positive and negative pressures within plenum ( 123 ). The positive and negative pressures generate attractive and repelling forces between platform structure ( 110 ) and support surface ( 20 ) causing platform structure ( 110 ) to levitate off support surface ( 20 ) in a stable, easily controllable manner.

Description:
CLAIM OF PRIORITY 
   This application claims priority from U.S. Provisional Patent Application No. 60/445,399 filed on Feb. 7, 2003. 

   FIELD OF THE INVENTION 
   The present invention relates generally, to levitating platforms. More specifically, the present invention relates to levitating platforms that can be used to safely and economically transport human beings, cargo, and other payloads over all kinds of terrain. The present invention can also be used as an attractor device to non-contactingly support work-pieces or provide a means for maintaining non-contact spacing between two objects. On a miniature scale, the present invention can also be used as a toy. 
   BACKGROUND OF THE INVENTION 
   Today, many types of aircraft, such as airplanes, helicopters, “wing in ground effect” (WIG) craft, gyrocopters, hovercraft, powered parachutes, etc. exist Some of these such as airplanes and helicopters are in widespread commercial use. However, no one type of aircraft has gained widespread personal use compared to the widespread use of other personal vehicles such as automobiles, motorcycles, snowmobiles, or personal watercraft. Well-known reasons such as high costs, extensive training requirements, limited accessibility, operating space requirements, and perceived safety risk account for the lack of widespread personal use of such aircraft. 
   Currently, the most commonly used vertical take-off or landing (VTOL) aircraft are helicopters and hovercrafts. However, these aircraft also have a number of well-known disadvantages, which have prevented their widespread use as a personal use aircraft. 
   As evidenced by the many prior-art patents on the subject, there has been a great deal of effort to develop a safe, inherently stable, compact, economical, easily portable, easily storable, easy-to-use, low-altitude flight-capable VTOL human/cargo transporter. For example, U.S. Pat. No. 2,953,321 to Robertson et. al. describes unique flying craft that was developed by the Hiller Helicopter Corporation in the 1950&#39;s, and became known as the Hiller Flying Platform. The Hiller flying Platform had limited technical success and was never commercialized. 
   Several other concepts exist for personal flying machines and/or unmanned aerial vehicles (that might be adapted for carrying people), which could be classed as “flying platform” craft. As described, these craft were supposedly capable of vertical takeoff and landing and free flight. Some of these concepts are described in the following US patents: U.S. Pat. No. 4,0043,421 “Air Car”; U.S. Pat. No. 4,47,024 “Airborne Vehicle”; U.S. Pat. No. 4,537,372 “VTOL Aircraft”; U.S. Pat. No. 5,026,002 “Helihover Amphibious Aircraft”; U.S. Pat. No. 5,152 478 “Unmanned Flight Vehicle etc.”; U.S. Pat. No. 5,178,344 “VTOL Aircraft”; U.S.Pat. No. 5,738,302 “Airborne Vehicle”; U.S. Pat. No. 5,803,199 “Lift Augmented Ground Effect Platform”; U.S. Pat. No. 6,082,478 “Lift Augmented Ground Effect Platform”; “Personal Air Transport”;; U.S. Pat. No. 6,464,459 “Lifting Platform With Energy Recover”. None of these craft concepts have been successful commercially, particularly in regards to being applied to a personal use aircraft. 
   To develop the invention claimed herein, the applicant has carried out extensive scale model testing of the inventive concepts described in some of the above-listed patents. However, the applicant was unable to experimentally substantiate the operating performance claimed in these patents because of fundamental flaws in the designs or underlying theories of the competing inventive concepts. 
   There is therefore a need for a personal aircraft which is capable of taking off and landing almost anywhere, is easy to fly, requires only minimal training to be operated safely, can be operated over any terrain, is inherently stable, is inherently safe, is easy to store and transport, is perceived by the general population to be safe, and is affordable. 
   SUMMARY OF THE INVENTION 
   In one aspect of the present invention, a levitating platform is disclosed which comprises a flow means for the passage of a fluid into a platform structure, which is arranged around the flow means. The fluid could be air, water or any other suitable fluid, which follows Bernoulli&#39;s principles. The flow means could be a flow conduit or a fluid pump such as a blower or a propeller fan or a turbine. The platform structure has an extended flow surface past which the fluid can flow during operation of the levitating platform. The extended flow surface can have any suitable contour such as flat, curved, geometric, or complex A protuberance boundary is arranged around the extended surface to deflect the flow of the fluid as it flows past the extended sure. During operation, the levitating platform is placed on a supporting surface so that a generally enclosed plenum is formed between the extended surface, the protuberance boundary, and the opposing surface. When the fluid is flowed into the plenum, it creates positive and negative pressure within the plenum. The positive pressure produces a repelling force between the levitating platform and the opposing surface causing the levitating platform to move away from the opposing surface. The negative pressure produces an attracting force between the levitating platform and the opposing surface causing the levitating platform to move towards the opposing surface. At any particular flow of the fluid, an equilibrium point is reached at which the attracting forces, the repelling forces, and external forces such as gravity are balanced. At the equilibrium point, the levitating platform is held in a stable manner at a constant distance away from the opposing surface. 
   In one aspect of the present invention, the opposing surface is fixed and the platform structure is allowed to move relative to the opposing surface. An application of this aspect of the present invention relates to a flying platform for transporting humans, cargo, and other payloads over terrestrial surfaces or for use as a toy. 
   In one aspect of the present invention, the platform structure has a geometric plan-form such as a circle, an oval, or a regular/irregular polygon. In another aspect of the present invention, the platform structure has a non-geometric plan-form. 
   In another aspect of the present invention, the flow means comprises a fluid flow port In another aspect of the present invention, the flow means comprises a fluid flow conduit, which is connected at its first end to the fluid flow port and at its second end to a source of fluid. In another aspect of the present invention, the source of fluid comprises a fluid-pump. In another aspect of the present invention, the fluid-pump comprises an air-fan. In another aspect of the present invention, the air-fan comprises propeller blades. In another aspect of the present invention, the air-fan comprises a blower impeller. In another aspect of the present invention, the air fan comprises a ducted air fan. 
   In another aspect of the present invention, the ratio of the area of the extended surface to the area of the fluid flow port is greater than 0.01 and less than 1000. 
   In another aspect of the present invention, the protuberance comprises a rigid material of construction. In another aspect of the present invention, the protuberance comprises a semi-rigid material of construction. In another aspect of the present invention, the protuberance comprises a lip. In another aspect of the present invention, the protuberance comprises a lift-enhancing element. In another aspect of the present invention, the protuberance comprises an airfoil element. In another aspect of the present invention, the protuberance comprises a ribbon. In another aspect of the present invention, the protuberance comprises a flexible skirt 
   In another aspect of the present invention, the levitating platform is used as an attractor to non-contactingly hold a work-piece at a fixed distance away from the levitating platform. In this application, the levitating platform is held fixed by any suitable conventional attachment means and the work-piece is allowed to move relative to the levitating platform When the fluid is passed into the plenum defined by the extended surface, the protuberance boundary, and the opposing surface of the work-piece, positive and negative pressure are created within the plenum. The positive pressure produces a repelling force between the levitating platform and the opposing surface causing the work-piece to move away from the opposing surface. The negative pressure produces an attracting force between the levitating platform and the opposing surface causing the work-piece to move towards the opposing surface. At any particular flow of the fluid, an equilibrium point is reached at which the attracting forces, the repelling forces, and external forces such as gravity are balanced. At the equilibrium point, the work-piece is held in a stable manner at a constant distance away from the levitating platform. 
   In another aspect of the present invention which is used as an attractor, the flow means comprises a fluid flow port and a fluid flow conduit connected at its first end to the fluid flow port and at its second end to a source of fluid. 
   Yet another aspect of the present invention discloses a method for the generation of attracting and repelling forces between a levitating platform and an opposing surface. In this aspect of the present invention, the levitating platform comprises a flow means for the passage of a fluid into a platform structure which is arranged around the flow means. The fluid could be air, water or any other suitable fluid, which follows Bernoulli&#39;s principles. The flow means could be a flow conduit or a fluid pump such as a blower or a propeller fan or a turbine. The platform structure has an extended flow surface past which the fluid can flow during operation of the levitating platform. The extended flow surface can have any suitable contour such as flat, curved, geometric, or complex. A protuberance boundary is arranged around the extended surface to deflect the flow of the fluid as it flows past the extended surface. The method includes the first step of placing the levitating platform on a supporting surface so that a generally enclosed plenum is formed between the extended surface, the protuberance boundary, and the opposing surface. The method also includes the second step of flowing the fluid into the plenum so that positive and negative pressure is created within the plenum. The positive pressure produces a repelling force between the levitating platform and the opposing surface causing the levitating platform to move away from the opposing surface. The negative pressure produces an attracting force between the levitating platform and the opposing surface causing the levitating platform to move towards the opposing surface. At any particular flow of the fluid, an equilibrium point is reached at which the attracting forces, the repelling forces, and external forces such as gravity are balanced. At the equilibrium point, the levitating platform is held in a stable manner at a constant distance away from the opposing surface. 
   These and other features, aspects, and advantages of the present invention will be better understood with reference to the following description and drawings wherein like parts have been given like reference numbers. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  represents an isometric general representation of a levitating platform according to the present invention.  FIG. 2A  represents a first equilibrium position of the levitating platform of  FIG. 1 . 
       FIG. 2B  is a graphical representation of the attractive and repulsive forces generated by the fluid flow in the first-equilibrium position of the levitating platform shown in  FIG. 2A . 
       FIG. 3A  represents the levitating platform of  FIG. 2 , which is in a temporary tilted operating position because of an external influence. 
       FIG. 3B  is a graphical representation of the attractive and repulsive forces generated by the fluid flow in the tilted operating position of the levitating platform shown in  FIG. 3A . 
       FIG. 4A  represents the levitating platform of  FIG. 1 , in a second equilibrium position. 
       FIG. 4B  is a graphical representation of the attractive and repulsive forces generated by the fluid flow in the final levitating position of the levitating platform shown in  FIG. 4A . 
       FIG. 5  is a graphical representation of the relationship between engine power consumption and levitating height as a function of the ratio of the extended area surface A 2  to the flow area A 1  of the fan in levitating platforms of the present invention. 
       FIGS. 6A  represents an isometric arrangement of a human transporting levitating platform prototype. 
       FIGS. 6B ,  6 C, and  6 D represent the plan-view, the longitudinal cross-sectional view, and the transverse cross-sectional view of the human transporting levitating platform prototype of  FIG. 6A . 
       FIGS. 7A and 7B  represent the transverse cross-sectional views of alternate configurations of the human transporting levitating platform prototype of  FIG. 6A . 
       FIGS. 8A to 8E  represent alternate configurations of the human transporting levitating platform prototype of  FIG. 6A . 
       FIGS. 9A ,  9 B, and  9 C represent alternate multi-fan configurations of the human transporting levitating platform prototype of  FIG. 6A . 
       FIGS. 10A ,  10 B, and  10 C represent the levitating platform of the present invention in its alternate application as an Attractor. 
   

   DETAILED DESCRIPTION 
   As defined herein, a “Levitating Platform” is a device, which operates on the basis of “Levitational Fluid Dynamics” principles. Levitational fluid dynamics principles relate to the ability of a fluid to create attractive and repelling forces between two objects. Using levitational fluid dynamics principles, the levitating platform can be made to operate in a Levitating mode wherein the repelling forces dominate to enable a freely moving levitating platform to move relative to a fixed opposing surface. Alternately, the levitating platform can be made to operate in an Attractor mode wherein the attractive forces dominate to enable a finely moving work-piece to move relative to a fixed levitating platform 
   The inventive concepts described herein have been validated by extensive model testing in the laboratory and out-door testing of a full-size prototype of a human transporting levitating platform. The levitational fluid dynamics of the present invention will be first described followed by a description of the bench-scale models and a full-sized prototype of a levitating platform that were built and tested by the applicant. 
   Through extensive cogitation and model-testing, the applicant has discovered novel principles of levitational fluid dynamics, which are explained with reference to  FIGS. 1 ,  2 A,  2 B,  3 A,  3 B,  4 A, and  4 B. 
   Refer now to  FIGS. 1 and 2A  which show a general representation of the levitating platform of the present invention.  FIG. 1  shows a general isometric representation of a levitating platform  10  which is configured as a disc  12  having a diameter D 2  and a concentric flow port  14  of diameter D 1 . Levitating platform  10  can be made of any suitable construction material such as plastic, wood, metal, etc. Disc  12  has an upper surface  12   a  and a lower surface  12   b . A lip  16  having a lower edge  16   b  is provided along the periphery of disc  12 . A flow means such as a propeller fan  18  having blades  18   b  is located within concentric flow port  14  to blow air downwardly through disc  12 . 
     FIG. 2A  shows a longitudinal cross-sectional representation of levitating platform  10  of  FIG. 1 . In this figure, levitating platform  10  is shown floating, in a, first equilibrium position above flat supporting surface  20 . Disc  12 , lip  16 , and supporting surface  20  cooperate to create a generally closed plenum  23  into which air  30  can be blown by propeller fan  18 . Air  30  is represented in  FIG. 2A  by dashed lines which represent the streamlines of air  30  as it enters through flow port  14 , flows through plenum  23 , and exits through gap  40  between lower edge  16   b  of lip  16  and supporting surface  20 . 
   For the sake of simplicity, levitating platform  10  has been shown as a circular plan-form shape in  FIG. 1A . However, levitating platform  10  could be configured with any other plan-form shape such as oval or rectangular, or square, or hexagonal, or any other regular or irregular geometric or non-geometric plan-form shape without departing from the spirit of the invention. Further, lip  16  can be any closed peripheral protuberance, which impedes the flow of air horizontally over lower surface  12   b  of disc  12 . Such a protuberance could be any shape, such as a ridge, a ribbon, a bump, etc. Alternately, the protuberance could also be any suitable aerodynamic shape, such as an airfoil to enhance the lift in the peripheral region of disc  12 . It is not necessary that the protuberance be located at the periphery of disc  12  as shown in  FIGS. 1 and 2A . The protuberance can be located anywhere between the periphery of port  14  and the outer periphery of disc  12 . 
   Also any suitable air-moving device, instead of a propeller fan, can be used as the flow means in levitating platform  10 , without deviating from the results discussed hereunder. It is not necessary that the air-moving device be attached to disc  12  as shown in  FIG. 1A . The air-moving device can be located remotely and the air could be communicated to concentric opening  14  by a suitable conduit Levitating platform  10  can also be operated on any fluid, which follows Bernoulli&#39;s principle, besides air as described with respect to  FIGS. 1 and 2A . 
   The area of lower surface  12   b  which is between the circumference of port  14  and the inner circumference of lip  16  is referred to as an “extended surface” in this description and clams. While this extended surface is shown as flat in  FIGS. 1A and 1B , it could have any contour such as flat, curved, geometric, or complex. 
   Refer now to  FIG. 2A , which shows levitating platform  10  in an first equilibrium position. It should be noted that the exact fluid dynamics, which result in the levitation of the levitating platform have not be fully determined. Therefore, the following description of the levitational fluid dynamics of the levitating-platform is quite hypothetical and could change with further empirical analysis. 
     FIG. 2A  shows the equilibrium position of levitating platform  10  when a small volume of air  30  is blown into plenum  23  by propeller fan  18 . As shown in  FIG. 2A , air  30 , represented by the dashed streamlines, flows through plenum  23 . However, lip  30  creates a resistance to the flow of air  30  within plenum  23 , which results in a build up of static pressure under the levitating platform. Lip  30  also causes the flow of air  30  to accelerate in the horizontal plane. Bernoulli&#39;s principle indicates that the increase in velocity will result in a reduction in pressure, which creates an attractive force between disc  12  and supporting surface  20 . It should be noted that lip  16  is important for achieving levitation. Without lip  16 , the horizontal velocity is high across all of the extended surface and the attractive forces are very high. Therefore, without lip  16 , the equilibrium height of the disc  12  from support surface  20  is very low. However, in a levitating platform application, it is desired that the equilibrium height of disc  12  from support surface  20  be high. Lip  16  produces a static lift which creates a repulsive force which somewhat negates the attractive forces and increases the equilibrium height of disc  12  from support surface  20 . 
   The presence of these attractive and repulsive forces has been demonstrated to provide greater stability to levitating platform  10  of the present art compared to lifting platforms of the prior art. For example,  FIG. 3A  shows levitating platform  10  when it is tilted to a non-equilibrium position by an external force such as a gust of wind. As shown in  FIG. 3A , the tilting of levitating platform results in a small gap  40   a  and a large gap  40   b  on diametrically opposite sides of disc  12 . The presence of large gap  40   b  reduces the resistance to the flow of air  30  on the high side of disc  12 . This reduction of resistance results in an increase in the horizontal velocity of air  30  towards larger gap  40   b  compared to the horizontal velocity of air  30  towards smaller gap  40   a . The higher horizontal velocity of the high side creates a lower pressure within plenum  23  in the region adjacent to larger gap  40   b . This lower pressure in turn creates a restoring moment which brings levitating platform  10  back to the first equilibrium position as shown in  FIG. 2A .  FIG. 3B  graphically represents the force distribution in plenum  23  during the tilted position of levitating platform  10  shown in  FIG. 3A . 
     FIG. 4A  shows levitating platform  10  when a larger gap  40   c  is created between lower edge  16   b  of lip  16  and supporting surface  20 . The presence of larger gap  40   c  reduces the static pressure within plenum  23 . With larger gap  40   c , the net force which attracts disc  12  towards the working surface increases relative to the repulsive forces which repel disc  12  away from the working surface  20 .  FIG. 4B  graphically represents the force distribution in plenum  23  when levitating platform  10  is in the elevated position of  FIG. 4A . The balance of the attractive and repulsive forces maintains levitating platform  10  in a more stable elevated operating position when compared to the elevated operating positions of lifting platforms of the prior art. 
   This above theory has been supported by testing of scale models and a full-size prototype of the levitating platform of the present invention. These scale models and full-size prototype have demonstrated much greater pitch, roll, and elevation stability than were demonstrated in lifting platforms of the prior art. 
   Applicant has empirically verified the presence of the attractive and repulsive forces described above in  FIGS. 1 ,  2 A,  2 B,  3 A,  3 B,  4 A and  4 B. Attached Tables  1 A to  1 C show the results of the verification experiments carried out by the applicant. 
   The scale models used for these tests were similar to levitating platform  10  described above in  FIG. 1 . Disc  12  was constructed of styrofoam. In the tests shown in Table 1A, air movement device  18  was a Zinger 14×4 wooden 2-bladed propeller fan which was modified to a 260 mm (10.25 inch) diameter. In the tests shown in Table 1B, air movement device  18  was a 63.5 mm (2.5 inch) propeller fan. In the tests shown in Table 1C, air movement device  18  was two sets of counter-rotating Zinger 14×4 wooden 2-bladed propellers. The propellers in all of the three sets of tests were driven by electric motors whose power consumption was measured using a voltage meter.  FIG. 5  shows the general representation of the relationship between engine power consumption and levitating height as a function of the ratio of the extended area surface A 2  to the flow area A 1  of the fan. 
   Based upon these tests, the applicant has demonstrated that the levitating platform of the present invention has more stable levitating performance than the lifting platforms of the prior art. 
   The following is a brief description of the constructional details of a prototype of a full-scale levitating platform that was built by and tested by the applicant in 2003. The levitating platform is intended for use as a human transporter but it could also be use for transporting cargo and other payloads. A miniature version of this prototype could also be used as toy. 
     FIG. 6A  shows an isometric representation of the prototype.  FIGS. 6B ,  6 C and  6 D show a plan-view representation, a longitudinal cross-sectional representation, and a transverse cross-sectional representation respectively of the prototype. The general configuration and operation of the prototype is similar to the configuration of the small-scale models described in  FIGS. 1 ,  2 A,  3 A, and  4 A. However, as will be described below, the prototype was adapted for human operation and transportation. 
   Referring to  FIGS. 6A ,  6 B,  6 C, and  6 D, human transporting levitating platform prototype (HTLPP)  100  comprises at least a platform structure (PS)  110  and an air-movement device  120 . Human transporting levitating platform prototype  100  also includes a rider support system  130  and a steering mechanism  140  even though these elements are not essential to the operation of human transporting levitating platform prototype  100 . 
   Platform structure  110  is configured as a wedge-shaped body  112  whose overall dimensions are 2.13 meters (7 feet) wide by 3.5 meters (11.5 feet) long by 0.6meters (2 feet) thick. Body  112  was contoured to provide a race-car like aerodynamic profile  115  at the top and a flat surface  116  at its bottom. A monocoque construction using fiberglass over polyurethane foam was used in the fabrication of body  112 . This particular wedge-shape was selected to provide an aerodynamic profile to monocoque body  112 . However, it will be obvious that other aerodynamic profiles would be used for monocoque body  112  without deviating from the spirit of the invention. 
   As shown in  FIGS. 6A ,  6 C, and  6 D, a lip  114  is attached to the lower surface  116  of monocoque body  112 . Lip  114  is constructed of nylon-reinforced urethane fabric and is attached to flat surface  116  by fasteners or some other suitable attaching means with a tight fit to the body to form a good seal. As previously described, lip  114 , and lower surface  116  of monocoque body  112  cooperate with support surface  20  to provide air-plenum  123 . 
   An air-flow port (AFP)  118  is provided in monocoque body  112  to contain the air movement device  120 . Air-flow port  118  is configured similar to a doughnut hole whose plan-view diameter is coincident with the major axis of monocoque body  112 . As will be described later, a set of propeller blades is located in air-flow port  118  to force air into plenum  123  during operation of human transporting levitating platform prototype  100 . 
   To provide optimal performance of the propeller blades, air-flow port  118  is configured similar to the scroll of a ducted propeller fan. Therefore, air-flow port  118  is configured with a bell-mouthed inlet  118   i , a straight cylindrical side  118   c , and a bell-mouthed exit  118   e . For optimal performance, the internal diameter “Dc” of cylindrical side  118   c  is selected to provide close clearance between the outermost tips of the propeller blades and internal sides of cylindrical side  118   c . Generally, a clearance of about 4 to 6 mm is contemplated to provide optimal performance of the propeller blades. Air-flow port  118  is reinforced with structural members (not shown) and a suitable lining of fiberglass or such other lightweight, high-strength material (not shown) as is typical in aircraft construction. To reduce damage due to entrained dust and other solid particles in the air, the lining can be further coated with a protective coating (not shown) of a hard composite material such as Kevlar. Alternately, the protective coating could be a metallic film. Such constructional techniques are well known in the art. 
   Air movement device  120  is mounted on monocoque body  112 . Air movement device  120  comprises a fan arrangement  122 , which is connected by a gear arrangement  124  to an internal-combustion engine  126 . 
   Fan arrangement  122  comprises a first 5-bladed fan  122   a  and a second 5-bladed fan  122   b . Each blade of fans  122   a  and  122   b  is 1,829 mm (72 inches) in diameter. Further, each fan blade  122   a   1  to  122   a   5  of fan  122   a  is independently adjustable in pitch Similarly, each fan blade  122   b   1  to  122   b   5  of fan  122   b  is also independently adjustable in pitch. Fan blades  122   a   1  to  122   a   5  are mounted on hub  122   c  and fan blades  122   b   1  to  122   b   5  are mounted on hub  122   d . Fan blades  122   a   1  to  122   a   5  and  122   b   1  to  122   b   5  and hubs  122   c  and  122   c  were procured from Warp Drive Products Inc., U.S.A. The hubs are made of aluminum and the propeller fan blades are made of carbon-fiber composite. However other materials of construction such as wood, aluminum, or fiberglass could also be used for the hubs and the propeller blades. Further, as is common in the art, the leading edge of the propellers can be coated with an abrasion resistant material such as Kevlar to reduce damage to the propellers from entrained dust in the air. 
   Hubs  122   c  and  122   d  are attached to the first ends  128   a   1  and  128   b   1  of counter-rotating concentric shafts  128   a  and  128   b  respectively. As shown in  FIG. 2   c , shaft  128   b  is configured as a hollow steel pipe while shaft  128   a  is configured as a solid steel rod, which is guided through shaft  128   b  to provide concentric operation. As will be described below, concentric shafts  128   a  and  128   b  are connected to the torque output side of gear arrangement  124 . Thus fans  122   a  and  122   b  rotate in opposite directions. Two counter-rotating fans were used in human transporting levitating platform prototype  100  because the prior art indicated that it would provide greater operating stability to the craft. However, subsequent scale-model tests have indicated that a single fan arrangement could provide an adequately stable operation. It is therefore contemplated that a simpler single-fan arrangement may be used in commercial versions of the lifting platform of the present invention instead of the 2-fan arrangement described above. 
   As shown in  FIG. 6B , gear arrangement  124  comprises three steel bevel gears  124   b ,  124   c , and  124   d , which are mounted in casing  124   a . First bevel gear  124   b  is attached to the output shaft  126   b  of internal combustion engine  126 . Second bevel gear  124   d  has a concentric bore for the through, non-contacting passage of shaft  128 a. Second bevel gear  124   c  and third bevel gear  124   d  are rotatingly coupled to first bevel gear  124   b  such that second bevel gear  124   c  counter-rotates relative to third bevel gear  124   d . As shown in  FIG. 6B , second bevel gear  124   c  is attached to second end  128   a   2  of shaft  128   a . Similarly, third bevel gear  124   d  is attached to the second end  128   b   2  of shaft  128   b . Thus, when first bevel gear  124   b  is rotating in a clockwise direction, it rotates second bevel gear  124   c  also in a clockwise direction and further rotates third bevel gear  124   d  in a counter-clockwise direction. Thereby, shafts  128   a  and  128   b , and consequently fans  122   a  and  122   b , also rotate in clockwise and counter-clockwise directions respectively. As will be obvious to one of ordinary skill in the art, suitable lubrication systems (not shown) can be incorporated in gear arrangement  124  to reduce friction-induced damage to the gears. 
   Internal combustion engine  126  is a 600 CC fuel injected motorcycle engine from a 1991 Honda F4 motorcycle. The maximum horsepower is estimated to be approximately 115 HP at the crankshaft The estimated power to the propellers after going through the motorcycle transmission and the custom built gear box is approximately 90 HP. Internal combustion engine  126  is mounted on structural support members (not shown) on monocoque body  112 . The torque output shaft  126   b  of internal combustion engine  126  is connected to bevel gear  124   b  of gear arrangement  124 . 
   Rider support system (RSS)  130  comprises a saddle  130   a , which is attached to levitating platform  112  by connecting structure  130   b . Rider support system  130  also comprised handlebars  130   h  for further support of the rider who maneuvers the craft by shifting his weight in the desired direction of movement. Alternately, handlebars  130   h  could also be attached to steering mechanism  140  for craft maneuverability. Alternatively, rider support system  130  could comprise a platform wherein the rider can stand while being transported. Yet further, rider support system  130  could comprise a chair or any other reclining device for tile support of the rider in a comfortable reclining position. 
   Steering mechanism  140  comprises paddles such as those described in the aforementioned patent to Robertson et. al. The design and construction of such steering mechanisms is well known in the art. Alternately, the craft can be yaw controlled by changing the pitch of the propeller blades in fans  122   a  and  122   b  to provide a differential torque. Human transporting levitating platform prototype  100  was tested in a California dry-lake bed near Edwards Air Force base by the applicant in 2003 and was found to have excellent stability, maneuverability, and altitude characteristics compared to lifting platforms of the prior art. As built and tested, human transporting levitating platform prototype  100  had the following statistics: Length 3.5 meters (11.5 feet); Width 2.13 meters (7 feet); Weight 327.3 kgs. (720 lbs) with fuel but excluding pilot; Pilot weight 82 kgs (180 lbs); Duct Area 2.65 sq. meters (28.5 sq. ft.); and maximum lower surface area 4.09 sq. meters (44 sq. ft.) which excludes duct area. 
   Applicant tested three variations of the configuration of human transporting levitating platform prototype  100 . These variations and tests are described below:
         Test 1: In this test, lip  114  was attached to the lower outermost perimeter of monocoque body  112  to provide approximately 4.09 sq. meters (44 sq. ft) squarish oval shape of lifting surface under monocoque body  112 .   In Test 1, human transporting levitating platform prototype  100  levitated at about 102 to 127 mm (4 to 5 inches) from the ground when measured from the bottom edge  114   b  of lip  114 . At this operating altitude, human transporting levitating platform prototype  100  was very, very stable. The rider&#39;s weight shift actions had a small effect on tilting the craft The levitating height did not increase noticeably with increased power. This variation of human transporting levitating platform prototype  100  took the least power to become airborne.   Test 2: In this test, lip  114  was moved inwards from the perimeter of monocoque body  112  to provide approximately 2.05 sq. meters (22 sq. ft.) approximately elliptically shaped lifting surface, which was slightly offset towards back of craft, under monocoque body  112 . Thus, air-plenum  123  under monocoque body  112  was slightly offset towards its back end.   In Test 2, human transporting levitating platform prototype  100  levitated at about 152 mm (6 inches) from the ground when measured from the bottom edge  114   b  of lip  114 . It was still quite stable but responded better to rider&#39;s weight shift actions than the variation in Test 1, which had a moderate effect on tilting the craft. The levitating height did increase a little with increased power. This variation took more power to become airborne compared to the variation of Test 1. The offset of air-plenum  23  gave human transporting levitating platform prototype  100  a bias for forward flight. When powered up, the human transporting levitating platform prototype  100  would tilt forward and accelerate forward modestly.   Test 3: In this test, lip  114  was attached further inwards from the perimeter of monocoque body  112  to provide an approximately elliptically shaped lifting surface of about 1.31 sq. meters (13 sq. f), which was very slightly offset towards the back-end of monocoque body  112 . Thus air-plenum  123  under monocoque body  112  was very slightly offset towards the back end of monocoque body  112 .   In Test 3, human transporting levitating platform prototype  100  levitated at about 203 mm (8 inches) from the ground when measured from bottom edge  114   b  of lip  114 . At this altitude, human transporting levitating platform prototype  100  was still stable. The rider&#39;s weight shift actions were fairly effective for tilting the craft. The levitating height did increase noticeably with increased power. This variation took the most power to become airborne. The slight offset provided a forward tilt bias as expected.       

   The tests of human transporting levitating platform prototype  100  indicate that the flight characteristics of the full size craft are very similar to the flight characteristics of the scale-models described previously. It is therefore contemplated that the performance of the scale-model is a good qualitative predictor for the performance of the full size craft. 
   It will be obvious to one of ordinary skill in the art that human transporting levitating platform prototype  100 , described above, is only one example of the various possible configurations that could be used for the levitating platform of the present invention without departing from the spirit of the invention. For example, as shown in  FIG. 7A , monocoque body  112  could be hollowed around air-flow port  118  to reduce weight. In such a configuration, a light-weight structural frame (not shown) of aluminum, fiberglass or other such light-weight high-strength structural members could be used for rigidity. The body of the craft could be a lightweight plastic or fiberglass membrane, which is attached to the frame. Yet further, as shown in  FIG. 7B , the body of the craft around air-flow port  118  could be a gas-inflatable bladder  119  of a suitable elastic fabric. Besides reducing weight, such construction would also allow for amphibious operation of the craft and reduce storage space requirements. Amphibious construction is well known in the art. Yet other modifications could be made to the above-described configuration of the levitating platform without departing from the spirit of the invention. For example, as shown in  FIG. 7A , lip  114  could be molded as an integral part of monocoque body  112 . To increase lift, lip  114  could be molded with a downwardly facing curved surface  114   a . Yet further as shown in  FIG. 7A , the basic levitating platform configuration can be modified with the addition of a peripheral flap/louver/tuning vane  114   f . The purpose of flap  114   f  is to increase the lift of the fluid flow at the boundary and hence provide more lifting force for a given level of power. It will be quite obvious that more than one set of flaps may be used in a “stacked” configuration to further enhance lift. The flap can be a simple curved plane in cross section or may have an airfoil type cross-section as shown in  FIG. 7A . Yet further, other air movement devices such as blowers and gas-turbines could also be used in the levitating platform of the present invention without deviating from the spirit of the invention. Yet further, multiple air blowing ducts could be used to increase the payload handling capacity of the craft. 
   While an internal combustion engine has been shown as the driving mechanism for the fans, other means of rotating the fans could also be practiced. For example, electric motors could also be used to rotate the fans. The electric motors could be driven by on-board batteries or fuel-cell systems. Alternately, turbine engines could also be used to rotate the fans. Such methods of rotating the fans are well-known in the art. 
   Further various other configurations of the levitating platform of the present invention can be practiced as represented in  FIGS. 8A ,  8 B,  8 C, and  8 D.  FIG. 8A  shows a configuration of the levitating platform of the present invention wherein the rider sits on a saddle  132  during its operation.  FIG. 8B  shows another configuration of the levitating platform of the present invention wherein the rider reclines in a chair  134  during its operation.  FIG. 8C  shows a configuration of the levitating platform of the present invention wherein the rider sits inside an enclosed, aerodynamically optimized canopy  136 . The levitating platform of  FIG. 8C  is further fitted with a conventional rudder  138  to facilitate the its steering  FIG. 8D  shows another configuration of the levitating platform of the present invention wherein the rider stands on a platform  146 , which has railings  148  for additional support of the rider.  FIG. 8E  shows yet another configuration of the levitating platform of the present invention, which has a payload area  142 . Other uses and configurations of the levitating platform of the present invention will be obvious to one of ordinary skill in the art. 
   It will also be quite obvious from the above description that multiple air-movement devices could be used in the levitating platform of the present invention.  FIGS. 9A and 9B  show levitating platforms of the present invention, which are configured with two air-movement devices  120 . Yet further,  FIG. 9C  shows a levitating platform, of the present invention, which is configured with four air-movement devices  120 . Auxiliary thrusting devices could be added to provide control means or to propel the platform Miniature versions of the configurations of the levitating platform shown in  FIGS. 8A-8E  and  9 A- 9 C can be used as toys with or without remote control capabilities. 
   The above description of the levitating platform of the present invention focuses on the levitational capabilities of a free floating levitating platform from a fixed support surface for use as a human and/or cargo transporter. However, the levitating platform of the present invention can also be used as an attractor to non-contactingly support work-pieces. In this mode of operation, the levitating platform of the present invention is held fixed while the support surface is allowed to move relative to the levitating platform. 
   As an example.  FIGS. 10A and 10B  show a levitating platform, according to the present invention, which is used as attractor  10 ′ to non-contactingly support work-pieces such as steel coils or computer chip wafers or a compact disc or similar object. 
   Attractor  10 ′ is similar in construction and operation to levitating platform  10  as shown in  FIG. 1 . Attractor  10 ′ also comprises disc  12  and lip  16 . However, as shown in  FIG. 10B , disc  12  of attractor  10 ′ is held stationary by any conventional attachment means  13  to prevent its movement. As shown in  FIG. 10B , work-piece  20   w  is allowed to move relative to attractor  10 ′. Work-piece  20   w  is non-contactingly held in an equilibrium floating position with a gap  40  between its surface  20   s  and edge  16   b  of lip  16  by the negative pressure created in plenum  23  (as described with respect to  FIG. 2A ) by the flow of a fluid therein. Work-piece  20   w  could be a steel sheet coil in a coil coating line or a computer chip wafer. 
   In the attractor embodiment of the present invention shown in  FIGS. 10A and 10B , a fluid  30  is supplied to plenum  23  through opening  19   b  of a fluid supply conduit  19 . However, a fluid movement device, such as air movement device  18  as shown for  FIG. 1 , can also be used to provide fluid  30  to attractor  10 ′. Fluid  30  could air, water, or any other suitable fluid which follows Bernoulli&#39;s principle. 
   As described previously for the embodiment of the present invention shown in  FIG. 1 , attractor  10 ′ will posses both repelling and attracting capabilities. As attractor  10 ′ is moved towards the opposing surface of work-piece  20   w , the net fluid dynamic equilibrium results in increasing repelling forces. As attractor  10 ′ is moved away from the opposing surface of work-piece  20   w , the net fluid dynamic equilibrium results in increasing attracting forces until the maximum attractive force is reached. As gap  40  between edge  16   b  of attractor  10 ′ and surface  20   s  of work-piece  20   w  is further increased, the attractive forces diminish. 
   In another aspect of the attractor of the present invention, fluid conduit  19 ′ and work-piece  20   w  are held fixed by conventional attachment means  13  and disc  12  is allowed to move relative to fluid conduit  19 ′ and work-piece  20   w . Fluid conduit  19 ′ is shaped similar to a nozzle with a tapered outlet section  19   t . Air  30  is flowed through inlet end  19   i  of fluid conduit  19 ′ and exits through outlet end  19   e  of tapered outlet section  19   t . The velocity of air  30  at outlet  19   e  is higher than at inlet  19   i  since the area of outlet  19   e  is less than the area of inlet  19   i . The diameter of outlet  10   e  is selected to be somewhat less than the diameter of flow opening  14  in disc  12 . Further, outlet  19   e  is positioned with a gap  19   g  from flow opening  14  in disc  12 . Air  30  exits outlet opening  19   e  and enters plenum  23 . The flow of air  30  in plenum  23  creates positive and negative forces within plenum  23 . However, since work-piece  20   w  and fluid conduit  19 ′ are held stationary by attachment means  13 , disc  12  moves relative to work-piece  20   w  and fluid conduit  19 ′ until it reaches an equilibrium floating position between work-piece  20   w  and fluid conduit  19 ′. 
   The applicant has been able to empirically demonstrate that each of the above configurations of the levitating platform of the present invention, which he tested as described in the preceding section of this description, possessed both repelling and attracting capabilities. The attractive capabilities were enhanced as the extended surface plan-form area is increased relative to the fluid inlet plan-form area and/or as the lip depth was decreased. 
   While the foregoing describes the use of one attractor of the present invention, it will be obvious that more than one attractor can be used to precisely position the work-piece in space. For example, one attractor can be positioned above the work-piece and the second attractor can be positioned below the work-piece. By varying the fluid flow-rate in each attractor, the attracting and repelling forces can be precisely controlled to move the work-piece to the desired equilibrium position in between the two attractors. Yet other numbers and arrangements of multiple attractors will be obvious to one of ordinary skill in the art. 
   It is contemplated that practical applications of the present invention will exist whereby both attractive and repelling capabilities will be useful. Besides, the examples given above, another example of the use of attractor  10 ′ of the present invention would be to provide non-contact traversing and surveying of an underwater vessel, such as a ship&#39;s hull or an off-shore drilling rig&#39;s submerged superstructure, at very close proximity. Yet another example of the use of attractor  10 ′ would be as a wall-walking or ceiling-walking carriage for a robotic tool to carry out repairs in hard to access places in buildings. A further example of the use of attractor  10 ′ would be as a wall-walking or ceiling-walking toy. 
   While the present invention has been described with reference to one or more preferred embodiments, which embodiments have been set forth in considerable detail for the purposes of making a complete disclosure of the invention, such embodiments are merely exemplary and are not intended to be limiting or represent an exhaustive enumeration of all aspects of the invention. Further, it will be apparent to those of skill in the art that numerous changes may be made in such details without departing from the spirit and the principles of the invention. The scope of the invention, therefore, should be defined solely by the following claims. 
   
     
       
             
           
             
             
             
             
           
             
             
             
             
             
             
             
             
           
         
             
               TABLE 1A 
             
             
                 
             
           
           
             
               GREEN SERIES TESTS 
             
             
                 
             
           
        
         
             
                 
               Number of Fans: 
                 1 
                 
             
             
                 
               Fan Diameter: 
               26.67 cm 
               10.5 inches 
             
             
                 
               Lip Height: 
               12.7 
                0.5 inch 
             
             
                 
                 
             
           
        
         
             
                 
                 
               Extended 
                 
                 
                 
                 
                 
             
             
                 
               Fan 
               Surface 
             
             
                 
               Diameter 
               Diameter 
                 
               Weight 
             
             
                 
               (cm)/ 
               (cm)/ 
                 
               of Test 
               Initial 
               Maximum 
             
             
                 
               Duct 
               (Extended 
               Ratio of 
               Levitating 
               Lift-Off 
               Lift-Off 
             
             
               Test 
               Area A1 
               Area A2) 
               Areas 
               Platform 
               Voltage 
               Height 
             
             
               No. 
               (sq. cm.) 
               (sq. cm.) 
               A2/A1 
               (gms) 
               (V) 
               (mm) 
               Observations 
             
             
                 
             
             
               1 
               26.7 
               26.7 
                 
               525 
               5 
               76 
               Unstable 
             
             
                 
               559 
               0 
               — 
                 
                 
                 
               Operation 
             
             
               2 
               26.7 
               26.7 
                 
               509 
               5.5 
               102 
               Unstable 
             
             
                 
               559 
               0 
               — 
                 
                 
                 
               Operation 
             
             
               3 
               26.7 
               56.5 
                 
               648 
               2 
               22 
               Extremely stable 
             
             
                 
               559 
               1950 
               3.49 
                 
                 
                 
               in pitch, roll and elevation 
             
             
               4 
               26.7 
               44.7 
                 
               610 
               2.5 
               22 
               Extremely stable 
             
             
                 
               559 
               1011 
               1.81 
                 
                 
                 
               in pitch, roll and elevation 
             
             
               5 
               26.7 
               34.7 
                 
               565 
               4 
               25 
               Extremely stable 
             
             
                 
               559 
               386 
               0.69 
                 
                 
                 
               in pitch, roll and elevation 
             
             
               6 
               26.7 
               32 
                 
               546 
               4.5 
               27 
               Extremely stable 
             
             
                 
               559 
               226 
               0.40 
                 
                 
                 
               in pitch, roll and elevation 
             
             
               7 
               26.7 
               30 
                 
               541 
               5 
               38 
               Extremely stable 
             
             
                 
               559 
               131 
               0.24 
                 
                 
                 
               in pitch, roll and elevation 
             
             
                 
             
             
               Notes: 
             
             
               Test 1: Model based on U.S. Pat. No. 6,464,459 FIGS. 100 and 201 using 6 inch diameter central disc and 4 stator blades to create toroidal flow as suggested by patent. 
             
             
               Test 2: Ducted fan model based on U.S. Pat. No. 6,464,459 FIGS. 800b without central disc. 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
           
             
             
             
             
             
             
             
             
           
         
             
               TABLE 1B 
             
             
                 
             
           
           
             
               BLUE SERIES TESTS 
             
             
                 
             
           
        
         
             
                 
               Number of Fans: 
                1 
                 
             
             
                 
               Fan Diameter: 
               6.35 cm 
               2.5 inches 
             
             
                 
               Lip Height 
               12.7 
               0.5 inch 
             
             
                 
                 
             
           
        
         
             
                 
                 
               Extended 
                 
                 
                 
                 
                 
             
             
                 
               Fan 
               Surface 
             
             
                 
               Diameter 
               Diameter 
                 
               Weight 
             
             
                 
               (cm)/ 
               (cm)/ 
               Ratio 
               of Test 
               Initial 
               Max 
             
             
                 
               Duct 
               (Extended 
               of 
               Levitating 
               Lift-Off 
               Lift-Off 
             
             
               Test 
               Area A1 
               Area A2) 
               Areas 
               Platform 
               Voltage 
               Height 
             
             
               No. 
               (sq. cm.) 
               (sq. cm.) 
               A2/A1 
               (gms) 
               (V) 
               (mm) 
               Observations 
             
             
                 
             
             
               1 
               6.4 
               36.8 
                 
               185 
               4.2 
               6 
               Very stable 
             
             
                 
               32 
               1034 
               32.64 
                 
                 
                 
               in pitch, roll and elevation 
             
             
               2 
               6.4 
               15.2 
                 
               135 
               4.2 
               6 
               Very stable 
             
             
                 
               32 
               151 
               4.76 
                 
                 
                 
               in pitch, roll and elevation 
             
             
               3 
               6.4 
               10.2 
                 
               126 
               8.7 
               10 
               Very stable 
             
             
                 
               32 
               49 
               1.56 
                 
                 
                 
               in pitch, roll and elevation 
             
             
               4 
               6.4 
               7.0 
                 
               125 
                 
                 
               Operation unstable 
             
             
                 
               32 
               7 
               0.21 
             
             
               5 
               6.4 
               6.4 
                 
               135 
                 
                 
               Operation unstable 
             
             
                 
               32 
               0 
               0 
             
             
               6 
               6.4 
               15.2 
                 
               135 
               4.2 
               6 
               Very stable 
             
             
                 
               32 
               151 
               4.76 
                 
                 
                 
               in pitch, roll and elevation 
             
             
               7 
               6.4 
               15.2 
                 
               135 
               4.2 
               6 
               Very stable 
             
             
                 
               32 
               151 
               4.76 
                 
                 
                 
               in pitch, roll and elevation 
             
             
               8 
               6.4 
               36.8 
                 
               185 
                 
                 
               Stable 
             
             
                 
               32 
               1034 
               32.64 
                 
                 
                 
               in pitch, roll and elevation 
             
             
               9 
               6.4 
               36.8 
                 
               185 
               4.2 
               13 
               Very stable 
             
             
                 
               32 
               1034 
               32.64 
                 
                 
                 
               in pitch, roll and elevation 
             
             
               10 
               6.4 
               26.7 
                 
               185 
                 
               19 
               Very stable 
             
             
                 
               32 
               527 
               16.64 
                 
                 
                 
               in pitch, roll and elevation 
             
             
                 
             
             
               Notes: 
             
             
               Test 4: Model not stable enough to test because of small extended surface. 
             
             
               Test 5: Lip placed at inside diameter of 6 inch diameter extended surface. Model not stable. 
             
             
               Test 8: Fan separated from disc. Fan air directed through flow opening in disc. 
             
             
               Test 9: Model supported upside down on downwards facing support surface. Attractive forces generated by model balanced the gravitational force and prevented it from falling down. 
             
             
               Test 10: Model operated in attractor mode to lift 10.5 inch foam disc weighing 42.5 grams at a gap of about 8 mm. 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
           
             
             
             
             
           
             
             
             
             
             
             
             
             
           
         
             
               EXHIBIT 1C 
             
             
                 
             
           
           
             
               RED SERIES TESTS 
             
             
                 
             
           
        
         
             
                 
               Number of Fans: 
               2(Counter-Rotating) 
                 
             
           
        
         
             
                 
               Fan Diameter: 
               36.195 cm 
               14.25 inches 
             
             
                 
               Lip Height: 
               12.7 
                0.5 inch 
             
             
                 
                 
             
           
        
         
             
                 
                 
               Extended 
                 
                 
                 
                 
                 
             
             
                 
               Fan 
               Surface 
             
             
                 
               Diameter 
               Diameter 
                 
               Weight 
             
             
                 
               (cm)/ 
               (cm)/ 
                 
               of Test 
               Initial 
               Max 
             
             
                 
               Duct 
               (Extended 
               Ratio of 
               Levitating 
               Lift-Off 
               Lift-Off 
             
             
               Test 
               Area A1 
               Area A2) 
               Areas 
               Platform 
               Voltage 
               Height 
             
             
               No. 
               (sq. cm.) 
               (sq. cm.) 
               A2/A1 
               (gms) 
               (V) 
               (mm) 
               Observations 
             
             
                 
             
             
               1 
               36.2 
               43.8 
                 
               703 
               4.8 
               32 
               Very stable 
             
             
                 
               1029 
               479 
               0.465374 
                 
                 
                 
               in pitch, roll and elevation 
             
             
               2 
               36.2 
               41.3 
                 
               694 
               5.2 
               38 
               Very stable 
             
             
                 
               1029 
               309 
               0.3004 
                 
                 
                 
               in pitch, roll and elevation 
             
             
               3 
               36.2 
               41.3 
                 
               687 
               5.5 
               38 
               Very stable 
             
             
                 
               1029 
               309 
               0.3004 
                 
                 
                 
               in pitch, roll and elevation 
             
             
               4 
               36.2 
               40.0 
                 
               685 
               5.6 
               38 
               Stable 
             
             
                 
               1029 
               228 
               0.221607 
                 
                 
                 
               in pitch, roll and elevation 
             
             
               5 
               36.2 
               38.7 
                 
               667 
               5.7 
               41 
               Stable 
             
             
                 
               1029 
               149 
               0.145275 
                 
                 
                 
               in pitch, roll and elevation 
             
             
               6 
               36.2 
               37.5 
                 
               662 
               5.9 
                 
               Unstable 
             
             
                 
               1029 
               73 
               0.071407 
             
             
               7 
               36.2 
               36.2 
                 
               657 
               6.3 
                 
               Unstable 
             
             
                 
               1029 
               0 
               0 
             
             
               8 
               36.2 
               41.3 
                 
               691 
               5.3 
                 
               Stable 
             
             
                 
               1029 
               309 
               0.3004 
                 
                 
                 
               in pitch, roll and elevation 
             
             
               9 
               36.2 
               41.3 
                 
               696 
               5.24 
                 
               Unstable 
             
             
                 
               1029 
               309 
               0.3004 
             
             
               10  
               36.2 
               43.8 
                 
               713 
                 
               51 
             
             
                 
               1029 
               479 
               0.465374 
             
             
                 
             
             
               Notes: 
             
             
               Test 8: Model fitted with 1 inch lip. 
             
             
               Test 9: Model fitted with 1.5 inch lip. 
             
             
               Test 10: Model fitted with 1 inch lip.