The Wimshurst machine is an "influence machine", an electrostatic generator that uses the charges already present on it to generate more charges by electrostatic induction. It does not rely on friction for its operation. Consider that the machine is charged as in the schematic representation, shown (with cylinders instead of disks) with each half of each disk with one polarity, with boundaries at the neutralizing bars. Ignore the charge collectors and the output circuit. The two neutralizer bars are shown floating, but it makes no difference in the operation if they are grounded. At top and bottom, the charges are opposite, and at the sides equal. With any small initial charge unbalance, the machine will quickly fall into this configuration. After this occurs, when a sector touches a neutralizing brush charge is attracted to it, with polarity opposite to the charges at the other disk, due to the influence of the electric field generated by the surrounding sectors. Since there are several sectors inducing charge in just one sector, more charge than is present in each of the opposite sectors is attracted, provided that the disks and sectors are at sufficiently small distance. The effect is that progressively larger charges are attracted to the neutralized sectors as the disks turn, and the voltages at all fixed sector positions grow exponentially. The buildup stops when the charge density on the sector surfaces creates an electric field intense enough to cause breakdown in the air around, usually just before they reach the neutralizing brushes. The machine then operates generating a constant current at the output circuit, with maximum voltage limited by sparking through the path formed by a series of sectors and a neutralizer rod, or by other losses in the structure due to insufficient insulation. Note that the induction from the adjacent sectors in the same disk is important. The sectors before a sector touching a neutralizer, and also the charge collector assemblies and sectors at the sides of the disks, generate intense electric field, and help in the induction. The sectors ahead have their prejudicial effect reduced by the oppositely charged sectors in the other disk. The machine is self-starting, because there is always some natural imbalance in the charges. The use of different metals in the sectors and in the neutralizing brushes helps the startup process due to contact potential developed when different metals touch.
The machine still works with just one disk turning, if the other is stopped and kept charged in some way. This idea is the base of the older machines of Holtz, Voss, and others, that use a rotating disk and a fixed disk with inductor plates. The elegant design of the Wimshurst machine uses the same disks to generate new charges and to induce charges, and keeps all the parts of the disks alternating polarity twice at each turn. This is important to avoid charge buildup at the unused sides of the disks, what in the machines with fixed inductors eventually reduce the induction effect and may cause periodical polarity reversals. The top and bottom of the machine operate at relatively low voltages, due to the opposite charges in the disk sectors at opposite sides. This reduces losses to the supporting structure and allows the upright supports, belts and pulleys to be positioned much closer to the disks than in other machines. At the sides of the machine, the disk sectors are charged with equal polarities, and far from the influence of the other side of the machine. A very high voltage appears, because the same charges generated at the top and bottom of the disks, where there is significant capacitance between oppositely charged sectors, are now widely separated, with low capacitance between them.
Collectors with metal points extract some charge to the machine terminals, that are so charged to the same voltage. A Faraday cage effect helps in the discharge of the sectors to the charge collectors. If the terminals are kept too far apart, eventually a spark will jump across the sectors in one of the disks and a neutralizing bar, discharging the machine. The maximum spark length is so approximately the sum of the sector spacings across a third of a disk (assuming the neutralizers at 60 degrees with the horizontal). Somewhat larger, because less voltage is necessary to cause a large spark than to cause a series of smaller sparks adding to the same length. The reason is that the sectors distribute the electric field more uniformly across the gap, reducing its maximum value. Due to this, the machine works better with many sectors than with few. 32 or 40 sectors are the usual, but 16 or 24 are enough for reasonable performance. The minimum is 8, maybe 6. Of course the shape of the terminals affects the maximum spark length, but the rule above works very well in the prediction of the maximum that can be obtained.
The maximum output current of a Wimshurst
machine depends essentially
on the area occupied by the sectors in the disks and on the rotation
speed. See how. In steady state, the machine
acts as a
current source for a load connected to its terminals, including
losses by internal corona and sparking. Curiously, practically
just one disk
contributes to the output current, because if the charge of one
sector is removed by a charge collector, the potential at the
corresponding sector in the other disk decreases due to the
relatively high capacitance between the disks, and the potential
difference between this sector and the charge collector becomes
too small for a discharge across the air interval separating
them. It is possible to collect charge from just one disk instead
of from both disks. The obtained current is a good fraction of
the regular output due to the same effect. It is even possible to
eliminate the neutralizer from the side where current is taken,
with the output circuit serving as neutralizer, but in this case
the machine is less reliable, requiring a short-circuit at the
output for startup and stops easily. There is a way to extract charge of
both disks, due
to Schaffers [p29].
charge collectors are displaced in the direction of the adjacent
neutralizers. This avoids the reduction of the potential at the sectors
in the other disk, and ideally doubles the output current of the
machine. The spark length is somewhat reduced, due to the smaller
distance between charge collectors and neutralizers.
Bright sparks require intense current. The current can be obtained by storing the charge extracted from the rotating discs in high-voltage capacitors (Leyden jars) connected across the machine terminals. The classical design comprises two Leyden jars with the insulated terminals connected one to each terminal, and the outer terminals interconnected. The spark gap usually consists of two metallic balls connected by metal bars to the charge collectors. Significantly longer sparks can be obtained by the addition of a smaller ball attached to the positive terminal. This increases the electric field around the positive terminal, forcing the ionization of the air to start at the positive side of the gap, instead of at the negative side, as happens with a symmetrical gap. The positive ionization forms a nice plume-like structure (that can be seen in the dark) pointing away from the positive terminal, that easily gets connected to the diffuse corona that the negative terminal emits. When the connection is established, a spark occurs, with the electrons flowing from the negative terminal to the positive. Short sparks are observed as bright straight lines. Longer sparks are more irregular, and may present branches, almost always in the direction of the negative terminal. In short sparks, the positive end is brighter, specially in sparks obtained without added Leyden jars, due to more concentrated current. In long sparks, the positive end is always a straight line perpendicular to the surface of the terminal, with the negative side irregular and a little brighter (why is a mystery). When the terminals are close to the maximum separation, "failed" sparks frequently occur. The charges that the spark formation drains from the terminals reduce the voltage between the terminals, and the spark is dissipated before completion. Larger capacitance in the Leyden jars can extend somewhat the maximum spark length, by providing more charge to complete sparks that would "fail". The addition of a smaller ball to the negative terminal is not effective. The electrons are ejected by the intense electric field, and disperse quickly through the air instead of forming an ionized path. This can be observed by a characteristic hissing noise. The smaller ball doesn't need to be electrically connected to the main positive terminal. It is still more effective if separated from the larger ball by a short length of insulator (a short plastic tube, for example). The small sparks between the larger ball and the smaller ball apparently increase the ionization around the terminal, and the separation reduces the loss of charge to the air (this I observed in my machines). In any case, the longest sparks are obtained with the neutralizers at high angle. Low angles increase the output current a bit . Small balls can be added to both terminals, and in this case the longest sparks are obtained with the positive terminal inclined in the direction of the negative . Another interesting gap structure is the ball-plane gap, that replaces the negative ball by a disk with rounded edges. This kind of gap requires less voltage to produce a spark, and can produce very long sparks.
The terminal balls shall correspond to the capabilities of the machine. A symmetrical gap with two spheres produces sparks with up to about 4 times the diameter of the spheres. A ball-plane gap goes to about 8 times the diameter of the sphere. Assuming that the maximum spark length is approximately the sum of the distances between adjacent sectors across a third of a disk, D, the balls can be dimensioned based on this, with balls with diameter D/4 for a symmetrical gap and D/8 for a ball-plane gap. A double ball gap can use this two sizes, maybe with the large ball larger. If the small ball is insulated from the large ball, it can be even smaller than D/8.
The operation of the machine can be analyzed quantitatively with the help of an electrostatic simulator. The simulation result below shows an idealized section of the disks, with three sectors in each disk, with the central sector e touching a neutralizer brush. The simulated sectors are rectangular plates with rounded surfaces, with 5 cm in length (direction perpendicular to the plane), width of 1.5 cm and spacing of 1.5 cm. The disk plates have a relative permittivity of 4, 0.25 cm of thickness and 0.5 cm of spacing. The sectors a, b, c, and d are initialized with a total charge of +10 nC in each. The sector e is grounded to 0 V (by a neutralizer brush), and sector f , having already passed under the neutralizing brush, has a charge identical to the charge in sector e. A series of simulations is performed with the charge in sector f varied until this condition is met. The simulation calculates the voltages at the sectors as Va = 11 kV, Vb = 5.9 kV, Vc = 3.0 kV, Vd = 11 kV, Ve = 0 V, and V f= -3 kV. The charge in sector e is found as -14 nC. The arrows showing the directions and relative intensity of the electric field show clearly that sector e is influenced by sectors a, b, and d, and this multiple influence is the cause of the charge gain of -1.4.
The machine can also be considered as a network of variable capacitors and switches, with capacitances from the sectors to ground and between all the pairs of sectors. The capacitances between sector pairs in the same disk are significant only between adjacent sectors. The capacitances between pairs of sectors in opposite disks vary periodically in the time taken for a turn, becoming large when they are facing each other and decreasing to practically zero when they are at two sectors or more of angular distance. The other capacitances, from sectors to ground and between adjacent sectors in a disk, vary too, but in a first approximation they can be considered fixed. The sectors are grounded periodically, in correspondence with the times when they touch the neutralizers, twice per turn. The output circuit adds another set of switches, connecting the sectors to the output at proper times. This circuit model can be simulated in standard circuit simulators. The picture below shows the result of a simulation of the startup of a Wimshurst machine with 16 sectors per disk, turning at 10 turn/second. The sectors are assumed to have 1 pF of capacitance to ground, 0.5 pF to adjacent sectors, 5 pF to the opposite sector, and 2.5 pF to adjacent sectors in the other disk. The voltages at three adjacent sectors and at the two 100-pF Leyden jars can be seen. The initial excitation was provided by ±10 V initially in the Leyden jars. In just three turns the Leyden jars reach ±184 V.
Antonio C. M. de Queiroz
Last update: 2 July 2014
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