The featured image is an electrical field intensity map for a Missouri Department of Conservation stream electrofishing boat. The boat is depicted as the white area; the two anode array fields are shown in red. Many thanks to Andy Turner of MDC for providing this graphic.
In electrofishing classes, Alan Temple often uses the term electrical net when discussing standardizing by power. The analogy is that a gill net, for example, can be of a fixed size – length, height, bar mesh – and construction and can be deployed the same way for standardized fishing. When we standardize by power in electrofishing, the objective is to produce the same size effective fishing zone for any water conductivity. That requires adjustments to the applied voltage, current and power in waters of different conductivity so that the same electrical power density in the water enters the fish and causes the desired fish capture response. But how large is the electrical net? This blog presents a method of calculating the size of the electrical net based on hypothetical but realistic values for a typical two-boom electrofishing boat with the boat hull as the cathode and with either Wisconsin rings or spider arrays for the anodes. Be aware; there will be formulas and calculations. Hang on, I think it will be worth it.
Let’s assume some values for the hypothetical two-boom electrofishing boat. A100 = 40 ohms, C100 = 12 ohms, Ca = 100 μS/cm where A100 is the resistance of one anode array at 100 μS/cm, C100 is the resistance of the boat hull at 100 μS/cm and Ca is the ambient water conductivity. The two booms are balanced as to resistance, are wired in parallel with each other and in series with the cathode. Thus, the total system resistance at 100 μS/cm, R100 = 40/2 + 12 = 32 ohms. The percent resistance (and voltage and power) to the anode is 20/32 = 62.5%. Let’s assume that the threshold applied current at match (115 μS/cm) is 10.0 amps, so the current applied to each boom anode array is 5.0 amps. However, that is at 115 μS/cm, and the ambient conductivity is 100 μS/cm. We can adjust threshold current to the ambient conductivity by using the Excel file EF Goals, by using an electrofishing tool phone app or by using the following formula:
It = 10.0 amps x (115+100)/230 = 9.35 amps total, or half that for each array, i.e. 4.675 amps per array. It is threshold current at 100 μS/cm. Note that we may “create” some extra significant figures for these calculations. Threshold voltage, Vt = 9.35 amps x 32 ohms = 299.2 volts. VAnode = 4.675 amps x 40 ohms = 187 volts. VCathode = 9.35 amps x 12 ohms = 112.2 volts. Or VAnode = 299.2 volts x 62.5% = 187 volts and VCathode = 299.2 volts x 37.5% = 112.2 volts. VAnode + VCathode = Total Voltage, i.e. 187 + 112.2 = 299.2 volts.
Now one additional value is needed before the calculations begin; that is the threshold field intensity, or voltage gradient (V/cm), at the ambient 100 μS/cm. For that, let’s rely upon the threshold power density at match, Dm, value suggested by Miranda (2005): 60 μW/cc for game fish at an effective fish conductivity, Cf, of115 μS/cm. Thus, the threshold field intensity at match,
Em = √(60/115) = 0.722 V/cm. That must be adjusted for 100 μS/cm via EF Goals, the phone app or by:
Et = Em x (Ca+Cf)/2Cf x Cf/Ca Et = 0.776 x (100+115)/230 x 115/100 = 0.776 V/cm.
From rearranging an equation in the last blog, the area of a watery surface out to a field intensity of Et is:
Total SA = (I x 1,000,000)/(Et x Ca) based on current or
Total SA = (V x 10,000)/(Et x R100) based on voltage.
Array SA = (IArray x 1,000,000)/(Et x Ca) based on current, or
Array SA = (VArray x 10,000)/(Et x A100) based on voltage.
Let’s use these formulas with our hypothetical but realistic values to calculate surface areas of our electrofishing net.
Total SA = (9.35 x 1,000,000)/(0.776 x 100) = 120,490 cm2 or
Total SA = (299.2 x 10,000)/(0.776 x 32) = 120,490 cm2
The SA of our net is the same with either the current or the voltage formula. The voltage formula for an array includes the voltage to an array, VArray. The two arrays are in parallel, so each array receives the same voltage, the anode voltage. In this case, VArray = 187 volts.
Array SA = (4.675 x 1,000,000)/(0.776 x 100) = 60,245 cm2 or
Array SA = (187 x 10,000)/(0.776 x 40) = 60,245 cm2
For our example, we are assuming that the two boom anode arrays are spaced far enough apart that they are acting independent of each other and far enough away from the cathode that their fields are not unduly influenced by it. Miranda and Kratochvil (2008) recommended anode array separation distances of about 1.9 m. One purpose of separating the anodes is to prevent electrically coupled fields, a situation to avoid. The calculated sizes of the electrical nets for each array are the same and are half that of the total net size.
It is relatively simple to calculate Total SA using either current or voltage if you have accurate metering for peak voltage and peak current to calculate the R100 value. To calculate Array SA using current, one needs to measure IArray which requires a peak reading current clamp or a current probe plus an oscilloscope. The procedure is simple and accurate. To calculate Array SA using voltage requires knowledge of VArray, A100 and C100. That, it turn, requires extra measurements or estimates and is more difficult to quantify accurately.
The field SA will vary with the waveform used. The 5 amps per array at match value used here is for a rectangular pulse with an “effective” frequency and duty cycle such as 60-120 Hz, 15-40% duty cycle. Rounded pulses or lower frequency or lower duty cycles likely require higher fishing thresholds and therefore will need a larger net because those waveforms generally are less effective for fish capture.
This has been a demonstration of how to calculate the electrical net size using a hypothetical example. A following blog will use real data to calculate the electrical net size of a two-boom electrofishing boat. Then we may look at other electrode designs.
Miranda, L. E. 2005. Refining boat electrofishing equipment to improve consistency and reduce harm to fish. North American Journal of Fisheries Management 25;609-618.
Miranda, L. E. and M. Kratochvil. 2008. Boat electrofishing relative to anode arrangement. Transactions of the American Fisheries Society 137:1358-1362.