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Electrical Net Size: A Two-Boom Boat Example

This information is from an electrofishing workshop held at Table Rock Lake, Missouri in June 2012 for the Missouri Department of Conservation. The aluminum electrofishing boat was 16 ft (4.9 m) long, and its hull was used as the cathode. There were two booms, each with Wisconsin rings of 83 cm diameter, and each ring had 11 metal droppers 22 cm long x 1.3 cm diameter. Distance from the center of the booms to the nearest boat hull waterline was approximately 250 cm.

Resistance was measured using an ETS MBS pulsator at 200 volts of 120 Hz, 15% duty cycle pulsed direct current. The applied current was 13.6 peak amps, and the ambient water conductivity was 264 μS/cm. Based on the above, the total system resistance, Rs = 14.7 ohms, and the resistance at 100 μS/cm, R100 was 38.8 ohms. Assume the current was evenly divided between the two anode arrays, so IArray was 13.6/2 = 6.80 amps.

The electrical field (voltage gradient, V/cm) profile was measured with a voltage gradient probe connected to an oscilloscope.

Measuring field intensity fore of the starboard anode array for a Missouri Department of Conservation electrofishing boat.

The resultant decay regression was Er = 277 x r-1.434 where Er was the predicted field intensity at distance r from the electrode array center with 200 volts and total 13.6 amps applied, which corresponded to 6.80 amps applied to that anode array.

Figure 1. Field intensity profile for a Missouri Department of Conservation electrofishing boat.

We have found from class field trips that setting a field intensity goal for successful fishing out 90 cm fore or lateral from an anode array center is a good starting point for applied voltage, current or power goal tables for Wisconsin rings or spider arrays. At match of 115 μS/cm, the field intensity target, Em, for game fish is 0.722 V/cm. This value can be adjusted to the ambient conductivity of 264 μS/cm using an Excel file called EF Goals, or from an electrofishing phone app or from the following equation:

Et = 0.722 x (264+115)/230 x 115/264 = 0.518 V/cm. This is the target field intensity at about 90 cm from the anode array center. We can use that value multiple ways to calculate the target applied current to the array. A simple way is to use it first requires a calculation of the field intensity at 90 cm with 6.80 amps applied and to then multiply the ratio of the target field intensity, Et, to the map field intensity, Er, times the 6.80 amps used for the profile map. Er = 277 x 90-1.434 = 0.437 V/cm. The target peak current to apply to each anode array, IArray is 6.80 amps x 0.518/0.437 = 8.06 amps at 264 μS/cm. Double that to 16.1 peak amps for the total applied current. The same thing could be done to calculate the target peak voltage, i.e. 200 volts x 0.518/0.437 = 237 volts. That is useful information for fishing. The same information can be used to estimate the size of the electrical net around an anode array. This can be done a couple of ways.

Array SA = (IArray x 1,000,000)/(Et x Ca) where Array SA is the area of a watery surface having at its outer edge a field intensity of Et. For this boat,

Array SA =  (8.06 x 1,000,000)/(0.518 x 264) = 58,939 cm2. This electrical net size is reasonably close to the value of 60,245 cm2 calculated for the hypothetical example in a prior blog.

Another way to calculate the electrical net size involves use of the field profile decay equation to create an equation for field size in surface area as a function of the radius r from the anode array center. The field profile map equation at 200 volts and 13.6 amps was Er = 277 x r-1.434. Let’s now investigate the coefficient, 277. A couple of equations given in prior blogs for calculating Er were (I x 1,000,000)/(SAr x Ca) and (V x 10,000)/(SAr x R100). For our purposes in this blog, let’s focus on the current-based equation — the first formula — and use IArray because the focus here is on the field size for one array. First, IArray x 1,000,000 / Ca is 6.80 x 1,000,000 / 264 = 25,758. Divide that by the 277 coefficient of the field profile equation to obtain 93.0. Therefore, the formula for the size of the electrical net becomes SAr = 93.0 x r1.434.  If r is 90 cm from the center of the anode array, Array SA = 93.0 x 901.434 = 59,002 cm2. This value is basically the same as the value calculated above (58,939) and close to the 60,245 cm2 value for the hypothetical example.

This may be somewhat circular reasoning if the 90-cm distance from the anode array center chosen for the field intensity goal is just a guess or is incorrect. To help evaluate the validity of using the 90-cm distance, let’s return to the estimation of the current and voltage goals and compare those to actual fishing thresholds with that boat using the ETS MBS pulsator with “effective” rectangular (square wave) pulsed direct current waveforms – 60 Hz, 25% duty cycle; 120 Hz, 20% duty cycle; and 120 Hz, 15% duty cycle. Our estimates of fishing target settings from the field calculations, without fish, were 237 volts and 16.1 total amps. The fishing thresholds using those waveforms were 198 to 260 volts and 15.0 to 17.5 total amps. Thus, the target or threshold estimates from the electrical field calculations were within the ranges of thresholds determined by actual fish catches. These were values for an ambient conductivity of 264 μS/cm. To convert the target total current to that at match, Im, use EF Goal, the phone app or Im = 16.1 x 230/(115+264) = 9.8 amps. From multiple electrofishing classes, the Im value for two-boom boats using rectangular pulses with “effective” waveforms of 60-120 Hz and 15-40 % duty cycle average about 10 peak amps total or about 5 amps per anode array at match of fish conductivity to water conductivity, i.e. at 115 μS/cm ambient water conductivity.

If the electrical net, or effective fishing zone around an anode array, is about 60,000 cm2, and this needs more evaluation, then let me offer two other equations for predicting applied voltage and current targets for electrofishing boats. First, we calculate Et, the target field intensity at a given ambient water conductivity. For game fish of approximately 20 cm or longer, use a field intensity at match, Em, of 0.722 V/cm. For smaller fish, the desired field intensity will be higher, but let’s just use the game fish value for now. Et = Em x (Ca+115)/230 x 115/Ca.  Use the following equations to calculate target applied current or voltage.

It = (Et x SA x Ca)/1,000,000 for total peak current and Vt = (Et x SA x R100)/10,000 for peak voltage.

Let’s assume SA = 120,000 cm2 and use that in an example. For Ca = 500 μS/cm, Et = 0.722 x (115+500)/230 x 115/500 = 0.444 V/cm. Let’s assume that R100 = 35 ohms, though this should be determined for a given boat and electrode configuration. For the given example, the applied current and target goals are:

It = (0.444 x 120,000 x 500)/1,000,000 = 26.6 amps and Vt = (0.444 x 120,000 x 35)/10.000 = 186 volts.

Note that both Et (decreases) and Ca (increases) change with increased Ca in the current target calculation whereas only Et (decreases) changes in the voltage target calculation.

More results should be calculated and compared to the theoretical net size value given here and for the hypothetical example presented in a prior blog. Early indications are that 5 amps applied to a variety of anode array configurations at match result in an electrical net of about 60,000 cm2. The electrical energy is dissipated in the water in various shapes depending upon the type and configuration of the electrodes and their proximity to one another. The electrical field equations presented here and in prior blogs may prove useful for calculating effective field sizes and for estimating current and voltage targets.

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