US1437183A - johnson - Google Patents

Description

E. E. JOHNSON.

MEANS FOR STABILIZING MOVING BODIES.

APPLICATION FILED NOV. 15. ISZI- I Patented Nov. 28, 192 2.

2 SHEETSSHEET 1- F/GJ.

E. E. JOHNSON.

MEANS FOR STABl'LiZlNG MOVING BODIES.

APPLICATION mm NOV. :5. 1921.

1 Patented NOV. 28,

2 SHEETS-SHEET 2.

Patented Nov. 28, 1922.

UNITED STATES EDMOND ERNEST JOHNSON, 0F MAIDENHEAD, ENGLAND.

MEANS FOR STABILIZING MOVING BODIES.

Application filed November 15, 1921. Serial No. 515,217.

To all whom it may concern:

Be it known that I, EDMOND En vnsr J OHN- SON, of Maescourt, Maidenhead, in the county of Berks, England, a British subject, have invented certain new and useful Improved Means for Stabilizing Moving Bodies, of which the following is a specification.

This invention relates to means for neutralizing forces acting laterally ina 'horizontal plane such, for instance, as centrifugal force or the effects of side winds, on a moving monorail vehicle.

According to this invention a monorail vehicle body is provided on each side with an aerotoil or cambered vane'mounted so that its angle of incidence may be varied about a vertical axis and constructed so that its camber may be varied towards either side of a neutral plane.

Each aerofoil is adapted to exert, when the monorail vehicle body is in motion through the air, a lateral force adapted to counteract a lateral force such as the centrifugal action set up when rounding a curve or the effect of a side wind, and for the purpose of conteracting such force as closely as possible each aerofoil may be set by hand, both with regard to its angle of incidence and with regard to its camber, but preferably automatically acting means would be provided to attain these ends. For instance, a servo-motor may be employed for varying the angle of incidence of the aerofoils, to theone side or the other, to counteract centrifugal force in rounding a curve the valve chests for permit ting the servo-motor to operate, in the one direction or the other, being controlled by a pendulum and a correspondingly moving arm geared thereto, whilst a servo-motor controlled by a pennant may be employed, in conjunction with the pendulum-controlled servo-motor, for a like purpose to counteract the effect of a side wind, and a servo-motor controlled by an aero-static device may be employed for varying the camber of the aerotoils to maintain the latter at their most efficient configuration according to the speed at which the monorail vehicle body is moving. The aerofoilsv are operated simultaneously and in the same direction so that when their angle of incidence is varied the force acting on the one would tend to push, and the force acting on theother would tend to pull, the vehicle body towards the inner side of the curve.

The aerofoils should be mounted so that their centres of pressure lie in or near the "transverse vertical and horizontal planes in aerofoils as set forth above a component of the resistance presented by each counteracts the laterally acting centrifugal or wind force.

If desired, and for the preservation of balance, when the vehicle body or'bodies is or are moving at speed, one or more additional aerofoils may be provided and mounted on each body so that the angle of incidence of each aerofoil is variable about an axis passing through the centre of gravity of the respective body. When more than one additional aerofoil is employed on a body, they may be operated simultaneously but may act in conjunction with each other thereby displacing a volume of air, on each side of the moving vehicle body of sufiicient mass to maintain lateral rolling equilibrium. Their controls may also be operated automatically through forces acting from the body at the point or points of contact with the supporting medium.

In addition to the stabilizing eflects which may be obtained the aerofoils may also be actuated so as to operate as brakes.

The accompanying drawings illustrate diagrammatically one method of carrying out the invention; Fig; 1 being a side elevation of a monorail vehicle, parts being broken away, and Fig. 2 being a plan thereof. 3 is a plan on a larger scale of the means for varying automatically the camber of the aerofoils, Fig. 4 is a transverse sectional elevation on a still larger scale of means for varying the angle of incidence of the aeroit'oils. Fig. 5 is a similar view of another portion of the means shown in Fig. 4, which portion has been omitted. from Fig. 4 for the sake of clearness whilst a servo-motor and its valve chests are shown in both Fig. 4E and Fig. 5 to facilitate comprehension of the relationship of the different parts; Fig. 6 is a detail view showing the pendulum and its associated parts in positions different from those shown in Fig. 4, whilst Fig. 7 is a sectional elevation on a still larger scale showing a detail of the'means illustrated by Fig. 3.

As shown in Figs. 1 and 2, a monorail vehicle has a semi-streamline body a and is provided with-tractor and pusher'propellers b and and track wheels d. At each side of the body a an aerofoil e is mounted so that its angle of incidencemay be varied about a vertical axis f situated near its leading edge,

a such, variation being effected automatically '1) a servo rnotor g, which is shown in both igs, 4and 5 and the piston hof which is connected by its piston rod j and a connect ing rod is, with a vertical crank shaftm at the a ,top of which is.a=bevel wheel a meshing with bevel wheelso, 0. each on a shaft pprojectingthrough the, body a near its top and at the, opposite end of which is a bevel wheel 9 meshing with a bevel quandrant a secured to the frame ofrthe aerofoil 6 so that movement of the pistonh, either; way from the midposi tionshown in, Fig; 4 will varythe angle of incidenceofithe, aerofoils e. e, in the one direction or the other.

The servo-motor g is controlled by a pendulnrn s within the body a which pendulum is subjected to centrifugal force, whilstthe action of the pendulum may be modifiedby a pennant t situated outside and above the body a, in the vertical plane of thetraclrwheel cl and abovethe widest part ofthe body, a which pennant is subected to the action of side winds and is balanced against. centrifugal force by a behweight a mounted on the opposite side of its spindle v and within the body a and ofthe requisite mass depending upon the distances of its centre of gravity from the axis ofthe, spindle o. In Fig. 1 the upper portion ofthe nearer aerofoil and part of the body a are broken away showing the pennant it, its bob-weight u and its spindle 'u in full 111165;;

The pendulum s is pivoted at w as high as possible and verticallyabove and parallel with the longitudinal axis of the bodya and its arm at is slotted as at 1 and formed at its. upper end witha toothed quadrant z meshing with a corresponding; toothed quadrant 11 formed at the lower end of an arm 12 pivoted at 13 and slotted as at 14. In the slots 7 and 14 are mounted slide blocks 15 and l6 united by connecting rods'17 and 18 with the piston rods 19 and 20 of piston valves 21, 22 and 23, 24 situated in valve chests 25, and 26 respectively. The valve chests 25 and 26 communicate from the middle of thelength of each with opposite ends of the cylinder of the servo-motor g by pipes .27 and 28 and the piston valves 22 and 24 normally close the inlet pipes 29 and 30 to, whilst the piston valves 21 and 23 normally close the exhaust pipes 31 and 32 from, the valve chests 25 and 26, it being understood that the inlet pipes 29 and 30 are connected with a suitable supplyof fluid under pressure (not shown) whilst, the exhaust pipes 31 and 32 are led away to a convenient location. 7

As the pendulum s swings to the one side or the other the arm 12 is moved correspondingly and the connecting rods 17 and 18 and valve rods 19 and 20 are moved in a the same direction, so that either the inlet pipe 29 and the outlet pipe 32 or the inlet pipeBO and the'outlet pipe 3:1areuncovered and fluid under pressure is; admitted to the one, side, and exhausted from; the other side,

of the piston h, which is consequently moved in the one directionor the other-to vary the angle of incidence of the aerofoils e. e. as hereinbefore set forth.

The slide blocks 15 and 16 are unitedxby a yoke 33, which is inturn united by a-connecting rod 34'with the piston rod 35' of'the piston 36 of a servo-motor cylinder 37, the opposite ends of which communicate by pipes 38, 39, with a valve chest 40 in which are disposedifour piston- valves 41, 42,43, 44,0navalve rod 45, The piston valves41 and 44 normally close inlet pipes 46 and 47 to, and the piston valves 42- and 43 nor? mally close exhaust pipes 48 and49 from,

the valve chest 40, and the valve rod'45 is. unitedby a connecting rod 50 with a crank admitting fluid under pressurev by way of vthe pipe 38 or the pipe 39 to one sideof the piston 36 in the servo-motor cylinder 37 and exhausting fluid from the other side of said piston by way of the pipe 39 or the pipe 38, according as the wind actsupon the pennant from the oneside or the other.

Movement of thepiston 3,6 in the servomotor cylinder 37 causes the blocks 15 and 16 to, be slidden up ordown in the slots 7 and 14 thus varyingthe leverage of the action of the pendulum soon the valve rods 19 and 20 as shown in Fig. 6 and modifying the valve opening to correspond with the algebraic sum of thependulum andpennant movements, e. the valve openingwhich should result from, a given amount of centrifugal action on the pendulum 8 may be augmented or decreased, as a result of wind action on the pennant t. That is to sayif the monorail vehicle body a be rounding a curve to the right centrifugal action Will cause it to lean to the left and the pen dulum s will consequently swing from its normal upright position to the left as shown in F 6 this will cause the inlet pipe 29 and the outlet pipe 32 to be opened (to an extent corresponding with the extent of swing of the pendulum s), and the outlet pipe 31 and the inlet pipe 30 to be closed thus moving the piston 7t and its rod 1' to the right so as to turn the vertical crank shaft m and shafts p. p to incline the aerofoils e, 6 towards the right to the required extent, the angles of incidence thus imparted tending to restore the vehicle body 0. to. its upright position. 1 If at the same time as the pendulum 8 thus swings to the left the pennant t be acted upon by a wind from the left, this will to some extent counteract the effect of centrifugal action, and consequently the angles of incidence imparted to the aerofoils c, 6, should be less. As a result of this wind action on the pennant t the inlet pipe 47 and outlet pipe d8 will be opened thus moving the piston 36 piston rod 35, connecting rod 34 yoke 33 and slide blocks 15 and 16 from their normal positions equidistant from the piv tal axes of the pendulum s and arm 12 upwards. The positions of the parts resulting from the combined action of a wind from the left and rounding a curve to the right is shown in Fig. 6. This reduces the leverage of the pendulum s on the connecting rod 17 and piston rod 19 thus causing the inlet pipe 29 to be opened to a smaller extent while the upward movement of the slide block 16 increases the leverage of the arm 12 on the connecting rod 18 and piston rod 20 thus causing the outlet pipe 32 to be opened to a great extent with the result that the angles of incidence imparted to the aerofoils e, c are less than would have been the case if there had been no side wind. Had the wind acting on the pennant '15 been from the right it would have augmented the effects of centrifugal action and to counteract this the inlet pipe 16 and outlet pipe 19 would have been opened with the result that the piston 36 and with it the slide blocks 15 and 16 would have been moved downwards from their normal positions equidistant from the pivotal axes of the pendulum s and arm 12, thus increasing the leverage of the pendulum s and decreasing the leverage of the arm 12 so that the inlet pipe 29 would have been opened to a greater extent and the outlet pipe 32 to a less extent than would have been the case if there had been no side wind, so that greater angles of incidence would be imparted to the aerofoils e, c. vSimilarly, if the vehicle be rounding a curve to the left the pendulum 8 would swing to the right and open the inlet pipe 36 and outlet pipe 31 to incline the aerofoils c. e, to the left; a wind from the left would to some extent augment the effect of centrifugal force and the opening of. the inlet pipe 47 and outlet pipe 18 and the consequent upward movement of the slide blocks 16 and 15 from their normal positions equidistant from the pivotal axes of the pendulum s and arm 12 would increase the leverage of the arm 12 and decrease the leverage of the pendulum s so that the inlet pipe 30 would be opened to a greater extent and the outlet pipe 31 to a less extent than would be the case if there were no side wind thus causing greater angles of incidence to be imparted to the aerofoils e, e, whilst if the wind be from the right the opening of the inlet pipe 46 and outlet pipe 49 and the consequent lowering of the slide blocks 16 and 15 from their normal midpositions would decrease the lever age of the arm 12 and increase the leverage of the pendulum s so that the inlet pipe 30 would not be opened to so great an extent and the outlet pipe 31 would be opened to a greater extent than would be the case if there were no side wind, thus causing the angles of incidence imparted to the aerofoils e, c to be decreased according to the strength of the side wind. It would appear that as the pennant t is the only controlling element on wiich side w'nds act directly and that as the effect of movement of said pennant is to cause an upward or downward movement of the slide blocks 15 and 16 from their normal mid-positions, such movement would be non-effective except when the pendulum s and 12 are displaced from their normal vertical positions as a result of the effect centrifugal action on the vehicle body a when rounding a curve, but it must be borne in mind that a side wind of suificient force to be taken into consideration would not only act upon the pennant t but would also tend to, and in fact. would, to some extent, cause the body a to lean over to one side or the other (to the right if the wind be from the left and vice versa) thus producing obliquity of the pendulum s and arm 12 and bringing about a corresponding setting of the aerofoils e, e to counteract the wind effect and right the body (6.

I is to be understood that the mechanism shown in Figs. 4 and 5 lie in the same or nearly the same plane and that they are shown separately merely for the sake of clearness.

In order that the camber of the aerofoils e 0 may be adjusted so that their configuration is the most efficient according to the speed at which the vehicle is travelling. and according to cent' ugal action on the bony a, each aerofoil e is hollow and has fixedly n'iounted therein a block or blocks. such as through a slot 53 in each of which passes 5% of a vertical crank shaft adapted to deform the walls of the aerofoil c and so adjust its camber. Each crank shaft 55 is connected by an extensible camber shaft 56(Fig. 7) with a crank shaft 57 (Figs. 3 and 7) and these crank shafts are disposed transversely of and near the bottom of the body a and are interconnected. by suitable gearing as at 57 so as to rotate in opposite directions. The cranks 58 and 59 of the crank shafts 57 57 are united by connectingrods 60 61 with the piston rods 62, 63 of servo- motors 64, 65, the cylinders of which are connected through pipes 66-67 with a valve chest 68 similar to the valve chests 25 and 26, except that the valve chest 68 has four ports instead of three. The valve chest 68 has two inlets 69, 70 for fluid under pressure connected with the casing 71 of a cock 72, said casing being connected by a pipe 7 3 with a source of fluid under pressure (not shown). The cook 72 has an admission port 74 extending through nearly 270 and a centrally escaping exhaust port 75 extending tl'irough nearly 90 and is operated by a pendulum 76. The valve rod 77 of the valve in the chest 68 passes slidably through the ends of a chamber 78 in which is centrally disposed a flexible diaphragm 79 to which said valve rod 77 is secured. Opening into the chamber 78 are two pipes 80 and 81, one at each side of the diaphragm 79, said pipes leading forwardly and projecting through the body a... the open end of the pipe 80 being covered by a cowl 82. As the vehicle moves forward the rush of air over the cowl 82 creates a partial vacuum in the pipe 80, whilst the air entering the open end of the pipe 81 sets up pressure therein with the result that the diaphragm 79 is deformed, the valve rod77 is moved and the ends of both pipes 69 and 70 are covered, to an extent depending upon the speed of the vehicle, the greater the speed the more said ends are closed. The pipes 69 and 66 are thus normally in communication with one another, as are also the pipes 70 and 67, and the aerofoils c c occupy the mid-position shown. in full lines in Fig. 3. The admission port 74 of the cock 72 is adapted, when said cock is turned in the one direction or the other, to establish communication between the pipe 7 3 and either the pipe 69 and therefore the pipe 66, or the pipe 70, and therefore the pipe 67,

thus admit-ting fluid under pressure to they cylinder of the servo-motor 64 or of the servo-motor 65 whilst the exl'iaust port 75 communicates with either the pipe 70 and therefore with the pipe 67, or with the pipe 69, and therefore with the pipe 66 and exhausts the cylinder of the servo-motor 65 or of the servo-motor 64.. i

The pendulum 76 which actuates the cock 72 being subject to centrifugal action serves to determine to which of the servo- motors 64 and 65 fluid under pressure shall be admitted and from which fluid shall be exhausted, and thus determines which shall.

central neutral chords, as indicated in Fig. 3.

Normally the pendulum 76 occupies a vertical position so that the inlets to both the pipes 69 and 70 are closed, when, therefore, the diaphragm 79 is deformed (to an extent which depends upon the speed of the vehicle) as a result of the pressure set up in the pipe 81 and of the partial vacuum created in the pipe 80 the valve rod 77 is moved but neither servo-motor 64 nor 65 is. operative and each aerofoil 6, remains symmetrical about its central neutral chord, as shown in full lines in Fig. 3, no rhat-terwhat maybe the speed of the vehicle and'the. consequent extent of deformation of the diaphragm .7 9. lVhen, however, the vehicleleans over to one side or the other under wind or centrifugal action, or both, either the inlet 69 or 70 is placed in communication with the pipe 7 3 according as the body a leans to "the right or to the left and consequently either the servomotor 64 or 65 is caused to actuate the crank shafts 57, 57, and 55, 55 so as to vary the camber of the aero-foils e e to, and adjust it on, the one side or the other ofthe central neutral chords, the extent to. which such adjustment takes place depending on'the extent of deformation of the diaphragmv 79 and consequent closure of the pipes 69 and 70, as a'result of the speed of the vehicle; the slower the speed the less the deformation of the diaphragm 7 9, consequently the less the closing of the pipes 69 and 70 and the more the movement of the pistons in the servo-motors 64 and65, so that the camber of the aerofoils e, e is greater the less. the speed. Thus assuming the cranks 58 and 59 to be in such an angular position in Fig. 3 (vertically upwards from their crank shafts 57, 57) that forward movement of the piston rod 62 will move the crank 58 forwardly and the crank 59 rearwardly, the crank shafts 55 of the aerofoils e, 6 will be moved clockwise and the variation of camber of the aerofoils e, e (and its adjustment) will be towards the left i. e. relatively to the direction of movement of the vehicle, as shown in dotted lines, whilst forward movement of the piston rod 63 will move the crank 59 forwardly and the crank 58 rearwardly and produce counterclockwise movement of the crank shafts 55, so that the variation of camber of the aerofoils e, e (and its adjustment) will be towards the right, i. e. relatively to the direction of movement of the vehicle as shown in dot and dash lines.

It is to be understood that the valve mechanism of the various servo-motors may include any known form of hunting gear, where required, in order to out off admisizing lateral forces acting on either side of said body when in motion, said means being adapted to exert in a horizontal. plan on either side of said body when in motion, forces opposed to said lateral forces, said means comprising two aerofoils or cambered vanes mounted on vertical axes and on either side of said body with their centers of pressure lying in the transverse vertical and horizontal planes in which lies the center of gravity of said vehicle, and means adapted to vary the angle of incidence of each aerofoil or cambered vane.

2. In a monorail vehicle the combination with the body thereofof means for neutralizing lateral forces acting on either side of said body when in motion, said means being adapted to exert in a horizontal plane on either side of said body when in motion. forces opposed to said lateral forces, said means comprising two aerofoils or cambered vanes mounted on vertical axes and arranged on-either side of said body with their centers of pressure lying near the transverse vertical and horizontal planesin which lies the center of gravity of said vehicle and means adapted to vary the angle of incidence of each aerofoil or cambered vane.

3. In a monorail vehicle the combination with the body thereof of means for neutralizing lateral forces acting oneither side of said body when in motion, said means being adapted to exert in a horizontal plane on either side of said body when in motion. 'forces opposed to said lateral forces, said means comprising a plurality of aerofoils or cambered vanes mounted on vertical and arranged in pairs on either side of said body in such positions that the resultant center ofpressure lies in the transverse vertical and horizontal planes in which lies center of gravity of said vehicle, and means adapted to vary the angle of incidence of each aerofoil or cambered vane.

4. In a monorail vehicle the combination with the body thereof of means for neutralizing lateral forces acting on either side of said body when in motion, said means heing adapted to exert in a horizontal plane on either side of said body when in motion, forces opposed to said lateral forces, said means comprising a plurality of aerofoils or cambered vanes mounted on vertical axes and arranged in pairs on either side of said body in such positions that the resultant center of pressure lies near the transverse vertical and horizontal planes in which lies the center of gravity of said vehicle, and means adapted to vary the angle of incidence of each areofoil or can'ibered vane.

5. In a monorail vehicle the combination with the body thereof of means for neutralizing lateral. forces acting on either side of said body when in motion, said means being adapted to exert in a horizontal plane on either side of said body when in motion, forces opposed to said lateral forces, said means comprising two aerofoils or cambered vanes mountedon vertical axes and arranged on either side of said body with their centers of pressure lying in the transverse vertical and horizontal planes in which lies the center of 'ravity of said vehicle, and means controlled by said lateral forces and adapted to vary the angle of incidence of each aerofoil or cambered vane.

6. In a monorail vehicle the combination with the bony thereof of means for neutralizing lateral forces acting on either side of said body when in motion, said means being adapted to exert in a horizontal plane on either side of said body when in motion, forces opposed to said lateral forces, said means comprising two aerofoils or cambered vanes mounted on vertical axes and arranged on either side of said body with their centers of pressure lying near the transverse vertical and horizontal planes in which lies the center of gravity of said vehicle, and means controlled by said lateral forces and adapted to vary the angle of incidence of each aerofoil or cambered vane.

7. In a monorail vehicle the combination with the body thereof of means for neutralizing: lateral forces acting on either side of said body when in motion. said means being adapted to exert in a horizontal plane on either side of said body when in motion, forces opposed to said lateral forces, said means comprising; a plurality of aerofoils or cambered vanes mounted on vertical axes and arranged in pairs on either side of said body in such positions that the resultantv center of pressures lies in the transverse vertical and horizontal plane in which lies the center of gravity of said vehicle, and means controlled by said lateral forces and adapted to vary the angle of incidence of each aerofoil or cambered vane.

8. In a monorail vehicle the combination with the body thereof of means for neutralizing lateral forces acting on either side of said body when in motion, said means being adapted to exert in a horizontal plane on either side of said body when in motion, forces opposed to said lateral forces, said means comprising a plurality of aerofoils or cambered vanes mounted on vertical axes and arranged in pairs on either side of said body in such positions that the resultant center of pressure lies near the transverse vertical and horizontal planes in which lies the center of gravity of said vehicle, and means controlledby said lateral forces and adapted to vary the angle of incidence of each aerofoilor cambered vane.

9; In a'monorailvehicle the combination Withthe body thereof of aerofoils or cambered vanespivotally mounted on said body in substantially vertical planes, and means for varying the degree of camber of said vanes according to the speed of the vehicle, said means being adapted to effect such variation on either side of a neutral plane.

10. In a monorail vehicle the combination with thebodythereof of aerofoils or cambered vanes pivotally mounted on said body in substantially vertical planes, meanscontrolled by thespeed of the vehicle for varyingthe degree of the camber of said vanes, and means for determining on which side of a neutral plane the camber of each vane shall be varied, said second mentioned means being controlled by lateral forces.

11. In a'monorail vehicle, the combination With-thebody thereof,of aerofoils or cambered vanes pivotally mounted on said body, the centersof pressure of said vanes lying in the transverse vertical and horizontal planes in which lies the center of gravity of the vehicle, a servo-motor connected with said aerofoilsor vanes for effecting a change of incidence thereof, a pendulum adapted under'the influence of centrifugal action to control said servo-motor, an auxiliary servomotor, adapted when operated to modify the action of the first mentioned servo-motor, and a pennant operable under the influence of lateral wind pressure to control said auxiliary servo-motor.

12. In amonorail vehicle, the combination with the body thereof, of aerofoils or cambered Vanespivotally mounted on saidbody, the centers of pressure of said'vanes lying near the transverse vertical and horizontal planes in which lies the center of gravity of the'vehicle, a servo-motor connected with said aerofoils or vanes for effecting a change of incidence thereof, a pendulum adapted under the influence of centrifugal action to bered vanes pivotally mounted'thereon, said vanes being so constructed that the camber thereof may be varied to one side or the other of a neutral position, servo-motors for varying the camber of said vanes and a 'dia phragm chamber for automatically controlling the amountof camber according to'the speed of the vehicle, the diaphragmin said chamber being controlled by air pressure exerted thereon, through tubes connected with said chamber on each side of the diaphragm, one of said tubes being provided with a cowl, substantially asdescribed.

14. In a monorail vehicle, the combination with the body portionthereoflof'a plurality of aerofoils or cambered vanes, mountedon vertical axes, servo-motors for "simultaneously varying the angle of incidence of said vanes, servo-motors for simultaneou'sly varying the camber of said vanes and: means for automatically controlling the operation of said servo-motorsin accordance with lat eral pressures of wmd or centrifugal action on said monorail body-to counteract the effect thereof.

15. In a monorail vehicle,the combination with the body "portion thereof, of a pluralit'y of aerofoils or cambered vanes, means for mounting said varies for varying the angle of incidence thereof, means for varying the camber of said vanes on either side of "a n'eutral position, servo motors for controlling the angle of incidence and camber'r'espectively andmeans automatically controlledby lateral windpressure and centrifugal action for controlling the action of Said servo motors, said servo-motor for varying the cambers of the vanes being also controlled by the speed of the vehicle;

EDMOND ERNEST JOHNSON.

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