The Physics & Calculations of the PowerSki JetBoard™of the G-Force Turn.

Thrust and Speed.  In order to achieve high speed performance, the water jet pump in the current jetboard must deliver sufficient thrust to quickly accelerate the craft and maintain its speeds preferably from 25 mph to in excess of 40 mph.  In order to overcome both the water's drag on the craft, and the air resistance of the rider and the jetboard. Both resistances, being proportional to the square of the speed, and the required thrust for achieving this range of speed, were calculated to be in the range of 130 to about 330 pounds.  In tests of the jetboard, a speed of 32-35 miles per hour was measured on flat water at a measured pump thrust of 240-265 pounds.

Weight and Engine Power. The primary power source, or engine, must have sufficient power to propel the weight (or mass) of the craft and rider to the desired range of speed of 25 mph to over 40 mph.  The required engine-delivered power depends on the energy consumed per second to move the combined mass of the rider and craft through the water at the desired speed.  This power is calculated from 1/2 the mass times the square of the speed, divided by the efficiency of the jet drive pump system.  For the desired range of speeds, and applicable range of rider plus craft weight between 250 lbs.minimum to about 400 lbs. maximum, engine power of 14 hp. to above 55 hp are required.  One attribute of the jetboard, is that a jetboard and rider weighing a total of 350 pounds, achieved a constant measured speed of 32-35 mph with an engine rated at 25 hp. output.  This relatively high weight requires high-powered engines, that are 30-50% of the total weight of the craft. That much engine weight requires precise placement within the hull in order to allow a rear-mounted rider to pivot the craft during turns without the use of a steering mechanism.

Buoyancy. The PowerSki Jetboard™ is designed to support it's own 100-150 lbs. plus a 250 lbs. rider, lying or standing behind the engine's location while the craft is moving at low speed before hydroplaning, without submerging the top of the engine compartment.  This is achieved by a precisely calculated craft volume, weight, and center of buoyancy relative to the longitudinal center of gravity.  Once hydroplaning is achieved, this natural, stationary buoyancy becomes less important, because the vertical force component on the rear of the jetboard is controlled by its thrust and speed.

Placement of the Mechanical Components (Center of Gravity). The jetboard's center of gravity (CG) is critical to its performance, stability and the capability of a rear-mounted rider to initiate and negotiate controlled, low and high speed turns without the use of a steering mechanism.  Control and, most importantly, maneuverability by a rear-mounted rider is achieved by positioning the jetboard's (mechanical) center of gravity (CG) on the craft's vertical longitudinal center plane, in front of the rider and at a horizontal distance in the range of 55%-85% of the bow.

A rider, whose weight typically will be 1 to 1.75 of the craft, stands in a sideways stance on the rear deck. The center of gravity (net CG) of the rider plus craft moves to a “sweet spot” position on the longitudinal center plane. Normally, the net CG is approximately below him between the position of his front and back foot.  In this case, the net center of gravity can be referred to as an “intelligent CG, because the rider is able to easily move the net CG with slight body movements to control the craft .  For example, during a take-off, the rider leans forward if in a standing position, or lies on the craft with his chest just behind the engine to move the net (“intelligent”) CG forward towards the hydroplaning position.  Then, the rider leans back, if standing, or stands up, if lying down, to move the net CG under his feet for stable high speed straight-line operation.  The rider turns the jetboard by slightly altering his weight distribution or position of his back foot (generally towards the rear) and in a transverse direction to the jetboard's longitudinal axis, into the direction of the desired turn.  This moves the net center of gravity to the rear and into the direction of the desired turn (left or right), placing the pivot point directly below the rider, thus producing a stable turn.  The rider can adjust the severity of the turn by the degree to which he shifts his body weight rearward and to the left or right of centerline.  The rider can negotiate both high speed, g-force turns and low speed turns which are described later. 

Precise location of the center of gravity is a key element of the PowerSki Jetboard™ and requires detailed calculations and design modification that take into account both the weight and weight distribution of an empty jetboard, and the weight and location of the mechanical components within the jetboard.  Unlike previous watercraft, the high-power engine dominates the total weight of the mechanical components, and its placement in front of the rider dominates the calculation of craft CG which is determined by calculating, each of three (3) orthogonal directions, the summation of the product of the individual masses times the distances from a reference datum, divided by the sum of the masses.

Even slight variations of the position of heavy components, like the engine, have a significant effect on the craft CG, as well as its performance and handling.  An innovation of the jetboard, is the positioning of the 59 lbs., 25 hp.engine assembly, and other mechanical components in the hull so that the jetboard's center of gravity is positioned at a distance of 62.5% of the total length from the bow, and about 1' in front of the net CG when a rear-mounted rider is in a typical stance for straight, high speed planing.  In order to achieve the desired handling characteristics, pivoting, stability, and speed for a rear-mounted rider, the jetboard's CG must be in the range of 55%-85% of the jetboard's total length, measured from the bow on the longitudinal axis, on the longitudinal vertical center plane, on the transverse axis, and about midway between the top and bottom hull on the vertical axis.

Bottom Hull /Rail. The hull's bottom design is critical to achieving controlled, high speed, high g-force turns, and low speed turns without the use of any steering mechanism or variable direction jet.  The hull features a unique combination of a flat hydroplane surface near the stern, and at the transitions through “V” shaped surfaces to the outer curved hyperbolic rails.  This design operates in conjunction with the net CG to enable stable transition from low speed startup to high speed, straight planing, and the easy initiation and execution of smooth,controlled high and low speed turns.  The unique combination of hull design features offers the rider optimal choices for operating in various situations.  During start-up, the abrupt hydrostep, bordering the hydroplane surface, facilitates instant release from the water when thrust is applied, resulting in an instantaneous transition to stable, high-speed hydroplaning where both the wet hull surface and its resulting drag forces are minimized.  The hydrostep, which varies from a negligible height at the forward initiation point of the hydroplane surface to a maximum height at the stern, can be a maximum of 1 to 4" high depending on its desired responsiveness during turns or maneuvers.  The hydroplane surface is generally shaped like a miniature surfboard.  It begins at a point located at the lowest portion of the hull at mid-jetboard, and proceeds aft without any vertical curve (“rocker”). This acts to resist vertical “porpoising” of the craft while lowering drag, and stabilizing the craft during high-speed operation.  The ‘V’ surfaces to the side of the hydroplane surface connect the base of the hydroplane surface with the outer rails.  The “V” – hydroplane interface lines are blended smooth forward of the jet pump intake to minimize aeration into the pump.  A sharp edge on the hydrostep begins at the forward edge of the jet pump intake and proceeds aft, thus promoting release of the water from tits sharp edges and reducing drag.  The full “V” shaped hull forward of the hydroplane surface assists the rider in initiating, quick “zig-zag” maneuvers with minimum effort.

The unique combination of high thrust, precision CG positioning, and hull bottom/rail configuration enables the jetboard and rear-mounted rider to negotiate stable, controlled high speed turns never before achieved on a stand up, rear mounted rider, personalized watercraft.  The rider will experience, during a turn, forces between 3 to 6 times the force of gravity.

This high centrifugal force allows the rider to negotiate high speed turns at approximate angles of his body to the water surface of 15° to 20° he is stabilized by both the upward vertical reaction force (equal to his weight times g-force times the sine of the angle) and the friction force of his feet on the craft (equal to his weight times g-force times the coefficient of friction (~0.2) acting against the downward force of his weight.  For example, a 200 lbs. rider would experience the following stabilizing forces acting against the vertically downward 200 pound force of his weight, thus preventing him from falling or slipping off the board as he negotiates a high speed turn.

The controlled and stable high g-force, 360° turn enabled by the PowerSki Jetboard™ has never been achieved in personalized watercraft or water skiing, when the rope's tension connecting the boat and the skier’s arm tends to produce destabilizing forces on the skier.

When the rider shifts his weight left or right to initiate a full turn, the jetboard rolls from the flat hydroplane surface, to the adjacent “V” surface, which increases in angle towards the bow, and provides the rider leverage to submerge the hyper-parabolic curve rail with his weight shift, thus initiating a turn.  The jetboard ends up gliding on the selected rail, proceeding from the stern portion to the mid portion of the rail for high speed turns and remaining on the stern portion of the rail in lower speed turns. The hydrodynamic drag forces on the submerged portion of the rail, in conjunction with the low center of gravity and pre-defined pivot point under the rider, produces controlled, smooth high and low speed turns with no abrupt movement to destabilize the rider.  The rails have a vertical upwards curvature (“rocker”) near the stern that riders can manipulate by shifting their weight to control the speed of the jetboard's response during turns.  In high speed turns the curved rail acts like a motorcycle tire by setting the final angle and direction of the turn.  The fins act to prevent over-rotation of the hull and prevent sliding during low speed and high speed turns.  As an alternative, low profile retractable “Bonzer” type fins can be used.

During low speed, tight-radius turns at speeds between 5-10 mph, the rider shifts the net CG aft and in the direction of the desired turn, sinking the aft end of the rail and simultaneously uses high thrust bursts of the water jet to accelerate through a tight (typically 3-4' radius) stable turn, pivoting the jetboard around the net CG without the use of a steering mechanism or moveable jet that's required by other watercraft.  A more extreme vertical spin maneuver in which a major portion of the jetboard is elevated out of the water  can also be achieved, by the rider shifting his weight and net CG even further aft by leaning backwards and applying maximum thrust of more than 200 lbs. A significant addition of thrust in the vertical direction will lift most of the jetboard out of the water.

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