Tesla Voltage vs. Sphere and Steamer Sparks

by
J.H. Couture
10823 New Salem Point
San Diego, CA 92126

author of The Tesla Handbook

Tesla coil builders have always used spark lengths to describe the output of their coils. A rough rule generally used is that the spark length will be 12 inches for each 400 to 500 watts input to the power supply. However, assigning a voltage value to a particular spark length has met with much disagreement and controversy. Some of the controversy is due to the confusion over the difference between sphere and streamer sparks in air. The following is an attempt to try and clear up this confusion.

The length of the spark for the same voltage will depend on the geometry of the electrodes. Large spheres will give the shortest spark and points will give the longest spark. The type of wave will also affect the spark length for the same voltage. The two most used types are the DC impulse wave and the continuous alternating sine wave. It is possible to accurately determine the peak voltages of these waves to assign a voltage value to a certain spark length. Tesla coil waves are not like either of these waves. Tesla waves are highly dampened sine waves that are erratic in nature. There is little uniformity in the wave on which to base test conditions. This can be verified with an oscilloscope.

It is important, therefore, in discussing voltage vs spark length to specify the type of electrodes and the type of waves used in the tests. For this discussion sparks using sphere electrodes will be called sphere sparks and sparks using all other types of electrodes will be called streamer sparks.

The greatest accuracy will be obtained with spheres. The spheres should have a diameter equal to or greater than the length of the spark. For voltages up to 2000 KV this means spheres with diameters up to 5 feet. The only published test data with these conditions have been made by high voltage labs that test utility VS Sphere and Streamer Sparks high voltage apparatus. The tests are made using impulse generators that produce DC impulse waves with known peak voltage values. The test results are shown in American and British electrical engineering books. There are no published test reports for Tesla coils at these high voltages and using these large spheres. Many researchers including Clark, Ryan, and Reukema have made high frequency spark tests but these tests were too limited in their test conditions.

Because the utility high voltage lab tests come closest to Tesla coil tests, this data was used to make the curves shown in the Tesla Handbook. How close these curves are to actual Tesla coil voltage cannot be determined until appropriate tests are made using Tesla coils and large spheres and the results published. The possibility of this data becoming available in the near future is remote because of the high cost of making these tests to 2000KV using large spheres.

The Tesla Handbook curves show a voltage of 1000KV to be a 20 inches spark using 5 feet spheres. These are actual test sparks using DC impulse waves. Note that the shortest sphere sparks are used in order If the to obtain consistent and accurate results. electrodes are changed to rod or points, this same voltage can produce streamer sparks of 30 to 60 inches depending on the type of electrodes used. As stated in the Tesla Handbook, streamer sparks can be two to three times the length of sphere sparks. It is obvious that spark lengths for the same voltage can vary substantially.

Air is a dielectric and insulating medium that breaks down under standard air conditions at 76000 volts per inch. The breakdown is due to the ionization of the air by the electric field that forms a conductive path between the energized electrodes. Ionization is a random event that creates a jagged conductive path giving the spark it's characteristic appearance. Because there is less diversion from a straight path with short sparks, the shorter sphere sparks are more reliable indicators of high voltages. The best spark control is obtained by the use of large spheres for Van de Graaff generators where large spheres are needed to contain the charge and prevent sparking.

If instruments are connected to the secondary terminal of a Tesla coil the loading of the coil will affect the voltage. One way of overcoming this problem is measure the voltage with an electrostatic voltmeter. This meter operates by sensing the electric field around the coil and does not have to connected to the coil. These meters are hard to find and expensive. They can be homemade using an operational amplifier but would require expensive instruments to calibrate. They can, however, be used without calibration to compare coils. Spark length represents peak voltages. These values are sometimes converted to RMS values when the test waves are alternating sine waves. Peak voltages are equal to 1.41 times RMS voltages.

The Tesla Handbook (p 13-2) describes a simple and accurate method for the amateur experimenter to measure the voltage of a Tesla coil. The method can be used at any voltage and is independent of all variables except voltage. The voltage can then be used as a means to calibrate spark lengths. Note that spark lengths are dependent on many variables. The method uses only a single sphere but a different sphere size is required for each voltage.

A common test for Tesla coils is to use a DC pulse from the rectified voltage of a transformer to energize a Tesla coil. The spark length will be found to be shorter than when using the same transformer to energize the coil with an alternating wave. One of the reasons for the longer spark with the alternating wave is that more energy is being supplied to the Tesla secondary. The alternating wave contains more energy than the DC impulse wave because it charges the primary capacitor more often (more breaks). This additional energy produces more voltage and spark in the secondary. The continuous application of voltage pulses to the spark conductive path also appears to be a factor in extending the spark length. This is why the type of wave must be specified when discussing all high voltage spark tests.

The Tesla primary and secondary circuits must be tuned to the resonant frequency to obtain the maximum secondary voltage. However, this is not a critical factor because the voltage vs spark length test is not a test for maximum voltage. If an out of tune condition exists, both the voltage and spark length will be less and this will be only a different point on the voltage vs spark length curve compared to the tuned condition.

There are several equations that can be used to compute the theoretical Tesla coil voltage. These equations are not of much use to the amateur experimenter because they all contain variables and efficiencies that must be estimated. Reasonable estimates of these variables cannot be made because there is insufficiencies Tesla coil test data available to make the estimates useful.

The reader should realize that this condensed description of complex phenomena is not the complete story of sparking in air. The mechanism of sparking in air and of atmospheric lightning, which is a similar phenomena, is not completely understood. Hopefully, the future will bring more answers. It is possible some of these answers will come from amateur experimenters who are Tesla coil builders.