The importance of low inductance
(from R.T. Hasbrooch, EE, PE)Regarding the importance of inductance Lightning, which is a current pulse, contains a broad spectrum of frequencies. The center of the power spectrum is about 4.5 kHz, with the upper limit reaching into the MHz range. Its peak return-stroke current is extremely large (10s of thousands of amperes), typically lasting for a hundred microseconds, or so. As the return-stroke current pulse flows through the resistance of the earth it produces a very large transient potential gradient across the ground. This potentially lethal gradient. Nominally 1,000 volts per meteris known as step voltage. However, even when the current is flowing in a substantial metallic conductor (i.e., one having a very low value of dc resistance) very large transient voltages are developed along the conductor. Although resistance may be very low, e.g., less than 10 ohms, the inductance (L)of the conductor (nominally 1.5 microhenrys per meter of conductor length) times the very high rate of change (di/dt) of the current pulse produces transient voltages reaching 100s of thousands volts, or higher (V = I*R + L* di/dt). So, despite the big emphasis on achieving a very low resistance ground, the inductive effect predominates, resulting in transient voltages significantly higher than those attributed to dc resistance of the grounding system. A lightning grounding system must be capable of accommodating extremely high peak currents, and present low values of resistanceand inductance. When grounding system resistance is tested, the equipment operates at a very low frequency. The result, which may look quite low, will actually be just the dc resistance component. Huge (i.e., deadly and damaging) transient voltages will be developed across the conductor while return-stroke current is flowing. Finally, consider a ten-meter section of heavy copper conductor connected to an earth ground. For lightning protection, two systems are bonded to it, one at each end of the section. The dc resistance between the two points is measured to be ten milliohms; the inductance is 15 microhenrys. A 50th percentile lightning return stroke of 24-25 kA, with acurrent rate-of rise of 40 kA/microsecond, flows through the conductor. Peak current times dc resistance produces approximately a paltry 240 V peak between the two grounded points. However, the peak transient voltage resulting from the conductors inductance is 600,000 volts! The two supposedly grounded systems are 600 kV apart, albeit only for a brief interval of time. Equipment damage and serious injury or death are definite possibilities, hence the reason for using single-point grounding. (Some discussion regarding this..) Is there any hope on a trailer sailer?If our cable hanging off the mast is 5 meter long down to the water and we assume that the cable iniated a discharge into the water (which then makes the water a low impedance - how low dont know). If the inductance of the cable is the same as used above (ie, 15 uh for a 10 meter long wire), then we could assume our cable hanging over the side has an inductance of 7.5 uh. Using the same numers as above, the voltage developed at the driving end of the cable (which is the bottom end of the mast) is give by the same equation:V = L*dI/dT = 7.5uh * 40ka/1usec = 300,000 volts or 3E5 volts. Ie, the bottom of the mast would develope 3E5 volts because of the current transient and assuming a perfect ground from the water. The height of the mast above the water is about 1.5 meters. So in this case, the electric field between the mast and the water would be 3E5/1.5 meters = 2E5 volts per meter. If the air breakdown voltage for air occurs at over 1e6 volts/meter, maybe there is some hope of at least disipating some of the charge fron the wires over the side before there is major flashover from the bottom of the mast to the water (which could use a human body to aid getting to the water).Of course, a major problem with this model is it assumes the impedance at the water is zero which is not true and the error will result in higher voltages at the mast. The Thomson web site discusses what these impedances are but its some brain damage to read...(Im pretty sure I will regret writing this stuff some day as its probably all incorrect but what the heck, I dont expect any one to beleive it anyhow..)