Prior blogs have described electrical fields from spheres and anodes such as Wisconsin rings and spider arrays. Most backpacks and push/tow barges employ anodes of a loop attached to a pole carried by the pulsator operator. A backpack loop may be a round rings (torus), a diamond or some other shape. Pointed loops allow getting into rock crevices or into brush cover where a round ring could not reach. However, the field is more intense from points versus from a round ring. Prod poles are used from boats in some situations where flooded timber or other obstructions would prove difficult to maneuver a boat with typical electrofishing booms. Prod poles are larger versions of backpack loops in both rod length and in loop diameter; they are held and maneuvered by someone on the boat bow while another person dips the stunned fish. They can be quite effective in tight spots. A caveat is that the operator is holding the anode while standing on the cathode boat hull. The human injury potential is greater than with a typical boom electrofishing boat, and fishing requires at least a three-person crew. This blog will discuss electrical fields associated with loops and estimates of their field size.

Let’s turn our attention to backpack field sizes. An ETS ABP-3 electrical field was measured in a fish raceway at Natchitoches National Fish Hatchery in 2012. The fiberglass raceway was 12.2 m long x 2.4 m wide and filled to a depth of 53 cm with 30.2 C water of 327 μS/cm ambient conductivity. The anode was held 33 cm off the bottom of the raceway. The applied voltage was 150 volts of a 60 Hz, 25% duty cycle waveform. Field intensity (voltage gradient) measurements were made with a voltage gradient probe attached to an oscilloscope. The calculated R100 value was 255 ohms. The cathode rattail was stretched behind the operator as for typical stream electrofishing.

Figure 1. Setup for measuring field intensity profiles in a raceway at Natchitoches National Fish Hatchery. An ETS ABP-3 backpack was used as the power source.

Figure 2. Closeup of the two anode shapes. One was a circular ring, and the other was a diamond. The PVC pipe held the loop in place for the field intensity (voltage gradient) measurements.

Two shapes of loop electrodes were used; one was round, the other was a diamond. Lateral (starboard) and fore measurements were made in the horizontal plane at the depth of the loops which were held parallel to the water surface and the raceway bottom. The field profile decay equations were:

Starboard Circular *E*r = 242 x r^{-1.836}, r^{2} = 0.9911

Starboard Diamond *E*r = 258 x r^{-1.841}, r^{2} = 0.9938

Fore Circular *E*r = 225 x r^{-1.818}, r^{2} = 0.9912

Figure 3. Field intensity profiles for the loop shapes and axis. Note the overlap in the three power regressions.

The Fore Diamond field differed somewhat from these three fields due to the pointed shape of the diamond in the fore direction, so that equation is not shown here. These equations are similar and strongly overlap, so only the field profile equation for the circular loop in the starboard axis will be used for calculations in this blog.

During class field trips and in other stream sampling, we have found that an applied current at match (115 μS/cm) of 1 amp is about threshold for most stream backpack sampling with an “effective” waveform such as 60 to 120 Hz, 15 to 40% duty cycle. Those waveforms work well for capturing warmwater fishes. Trout sampling generally is done at 30 Hz to avoid injury; the threshold current for 30 Hz may be higher than 1 amp. Miranda (2005) recommended for boat electrofishing of fish at least 20 grams an in-water power density of 60 μW/cc at match. The associated field intensity is sqrt(60/115) = 0.772 V/cm. Based upon fish length-frequency equations, 20 g fish are about 12 cm in length. The electrofishing net size for these assumptions and this size fish is: SA = (1 x 1,000,000)/(0.722 x 115) = 12,044 cm^{2}.

Smaller fish require a large field intensity for immobilization. Based upon Figure 1 of Miranda (2005) plus use of fish length- frequency equations, let me suggest the following power density values for smaller fish; 200 μW/cc at match for 3-5 gram fish (7-8 cm) and 300 μW/cc at match for fish 1 gram or less (5 cm). A power density of 200 μW/cc equates to 1.32 V/cm, and 300 μW/cc equates to 1.62 V/cm. The associated electrical net sizes for these fish sizes when using 1 amp at match are:

SA = (1 x 1,000,000)/(1.32 x 115) = 6,588 cm^{2} for 7-8 cm fish, and

SA = (1 x 1,000,000)/(1.62 x 115) = 5,369 cm^{2} for fish 5 cm or less

Note that the field size decreases substantially for fish smaller than 12 cm. Conversely, the field size increases for larger fish. The threshold power density at match for larger fish may be 20 or even 10 μW/cc at match. Such an adjustment is more apt for boat electrofishing than for sampling relatively small stream fishes with backpack electrofishers.

The above equations estimate the surface area of the effective fishing zones, the electrical net sizes, around the loop anodes for three sizes of fish given the same applied voltage and current. It may be useful to also estimate the radial extent, in the lateral and forward directions, of the effective field. How far does the field reach from the center of the loop? To do that, let’s adjust the field profile equation to that at match. We need to know the applied voltage at match to adjust the equation. There are multiple ways of calculating that voltage. Here is one: Vm = 150 x 230/(115+327) x (327/115) = 222 volts. Adjust the field profile equation coefficient in proportion to the voltage change from what was used to create the initial regression. Thus, 222/150 x 242 = 358. The profile equation adjusted to 22 volts at match is 358 x r^{-1.836}. Now calculate (1 x 1,000,000)/115 = 8,696 and divide that by the profile regression coefficient, 358. The result, 24.29, becomes the coefficient of the surface area equation, and the sign of the exponent is changed. Let 12,044 cm^{2} = 24.29 x r^{1.836}. Therefore, r = 29.4 cm. The implication is that the effective zone for immobilization (or capture?) of 12 cm fish extends 29.4 cm (11.4 inches) from the loop center. Of course, that depends upon the length of time the fish has been exposed to the current, the actual size of the fish, the direction it was facing in relation to the anode, whether the fish was moving or still, cover, operator/dipper skill and a host of other factors. The zone of taxis or inhibited swimming likely extends farther out than this 29-cm electrical net, and larger fish likely are affected at farther distances. Still, this procedure provides a more objective way to quantify the size of the electrical field around an anode.

We can use the same procedure to find the effective radial distance for the other fish sizes with the same applied voltage and current. Just substitute the respective SA values on the left side of the equation. For 7-8 cm fish, the distance is 21.2 cm (8.3 inches); for fish 5 cm or less, it is 18.9 cm (7.4 inches), based upon these calculations and assumptions. Those small fields and consequent short distances may not be acceptable. One can increase the applied voltage and current to increase the field size. For a given electrode configuration, water conductivity and water depth — barring any strange situation such as conductive substrates — the electrical resistance will remain the same, so increasing voltage say 20% will also increase the current 20%. The relationship among volts, amps and ohms is Ohms Law. For the 7-8 cm fish, increase the applied voltage so that the current at match increases to 12,044/6,588 x 1.0 = 1.83 amps at match, based on the relative electrical net sizes using the same voltage and current for both fish sizes. Similarly, for the 5-cm fish, the voltage is increased to 12,044/5,368 x 1.0 = 2.24 amps at match.

In a prior blog of this series, for a boat using 5 amps per anode at match, the electrical net size was 60,245 cm^{2}. Now, for this backpack example using 1 amp at match, the net size is 12,044 cm^{2}. Using one fifth of the current results in one-fifth of the net surface area. Net size is directly proportional to applied current for the same water conductivity. In fact, net size is directly proportional to applied voltage regardless of water conductivity, but the R100 and A100 values must remain constant. Those are the total resistance and the anode resistance, respectively, at 100 μS/cm.

This may be a good place to mention that water depth affects electrical fields. Assuming non-conductive substrates (see a prior blog about conductive substrates), the electrical energy is compressed vertically when one moves to shallow water; the resistance increases and the current decreases. However, some compensation occurs because the field may expand more radially from the electrode when in shallow water because the vertical extent of the energy dispersion has been reduced. This vertical field compression is called a boundary effect; the water surface and/or the bottom substrate can cause a boundary effect. Even a cliff or other close lateral obstruction can act as a boundary to the movement of electrical charges. Water depth can affect profile maps and fishing. In a class in Ft. Collins Colorado, a backpack operator stood in water of about 40-60 cm while we adjusted the backpack current to 1 amp. When he walked near the shoreline, the current dropped to about 0.5-0.6 amps as the boundary effect became apparent and the resistance increased. The electrical field likely spread out more radially from the loop. Therefore, there is some compensation on fishing for the reduced vertical extent of the electrical field. This approach has been used successfully for backpack fishing: Once at the site, put the anode in water of 40-60 cm, if possible, with the anode loop held at mid depth, then adjust the current to 1 amp at match; this requires measuring the ambient conductivity and the ability to make the proper amp calculation based on that conductivity. Then fish for a few minutes to make any small adjustments to reach fishing threshold, then lock in that voltage and go fishing. Movements to shallow water will be compensated for fishing to some degree by the increased lateral extent of the field as the vertical extent is reduced. Moving to a deep pool reduces resistance and increases the electrical current. The increased amp draw may overload the backpack; that is another story beyond this blog. If you will be in very shallow water for the entire sampling trip, then it may be advantageous to set the current to say 0.6 amps at match in shallow water at the outset and adjust slightly as needed. The R100 value in shallow water is much higher than the typical 250-350 ohm value for backpacks in somewhat deeper water. Oh, here is a quick, simple method for estimating the target applied current if starting in 40-60 cm water where 1 amp at match is the target. Take the ambient conductivity, Ca, then use this approximation: I = (Ca+100)/200. You can easily do this in your head. For example, if Ca = 240 μS/cm, then I = (240+100)/200 = 1.7 amps. Using the “real” formula, the answer is 1.54 amps.

Other uses of electrofishing with loops are when using a tow or push barge and when using shore-based electrofishing. These uses likely are electrically similar in terms of the fields per loop anode, but the shore-based system may employ more loops. The first push barge electrofisher we had the opportunity to investigate was one brought to a class at Loxahatchee National Wildlife Refuge in Florida. It was brought by Karl Anderson of the USGS Columbia Environmental Research Center in Columbia, Missouri. The information presented below is from Karl, from Alan Temple and from my notes. We made resistance measurements in Florida, but here I’ll use other information which Karl provided from a subsequent fish sampling trip. The barge was built by Midwest Lake Electrofishing Systems (MLES) and was powered by an MLES Infinity boat pulsator. The cathode was a 168 x 114 cm flat plate mounted on the bottom of the barge away from accidental human contact. The barge could be operated with one or two loop anodes, each on poles with individual safety switches. The barge operator, who pushed the barge, manned the pulsator controls and meter output. For threshold testing, the Infinity was set to an 80 Hz, 40% duty cycle rectangular (square-wave) pulsed direct current. Threshold testing was conducted in water of 715 μS/cm ambient water conductivity, and one anode loop was used. Threshold voltage and current were 191 volts and 9.3 amps, respectively. Thus, the system resistance was 20.5 ohms, and the R100 value was 147 ohms. Threshold current of 9.3 amps at 715 μS/cm equates to an Im value of 2.58 ohms. The target fish for this barge were small Silver Carp, but let me change the Em value to 0.722 V/cm to match other calculations in this series of blogs on electrical fields. The target field intensity at 715 μS/cm was 0.419 V/cm. The electrical net size, SA = (9.3 x 1,000,000)/(0.419 x 715) = 31,043 cm^2 using current or SA = (191 x 10.000)/(0.419 x 147) = 31,010 cm^2 using voltage. Karl mapped the electrical field. If I followed the notes correctly, the extent of the field to the target field intensity was 65.6 cm. The notes indicate that the R100 values for operation with one and two loops were 147 and 87 ohms, respectively. Based upon those values, the A100 was 120 ohms and the C100 was 27 ohms. Those values are the resistance of one anode and the cathode, respectively, at 100 μS/cm ambient conductivity. The percent of power to the anode with one loop was 82% and with two loops was 69%. A reasonable starting Im value for stream fishing, based upon these results may be 2.5 amps at match per loop, i.e. 5 amps for two anode loops. For this barge, that translates to about 320 and 380 volts at match for operation with one and two loops, respectively. The estimated field size using the equivalent of 2.58 ohms at match equaled 31,043 cm2. If the starting Im value were 2.5 ohms, the calculated field size would be 30,080 cm2. Remember that value for use in the last blog of the series.

Prior blogs in this series have mentioned using the re-constructed electrode field profile data from Kolz (1993) for spheres and for Wisconsin arrays. He also measured voltage by distance using loops. Here are the results generated from the analysis of those data.

__61 cm dia x 1.27 cm stock loops__: R100 = 46 ohms. The field intensity profile equation for 5 amps applied was *E*r = 8746 x r^{-2.104}. Bypassing all of the calculations, the surface area formula at match, with 5 amps applied, was SA = (5 x 1,000,000)/(0.722 x 115) = 60,219 cm^{2}. Surface area by distance from the loop center was SA = 4.971 x r^{2.104}. The distance to the target field intensity was r = 87.2 cm.

__36 cm dia x 0.64 cm stock loops__: R100 = 86 ohms. The field intensity profile equation for 5 amps applied was *E*r = 4628 x r^{-1.985}. The surface area was the same because both used 5 amps at match. The formula for surface area by distance was SA = 9.394 x r^{1.985}. The radial distance to 0.722 V/cm was r = 82.8 cm.

For backpacks, the distance to the threshold field intensity was about 29 cm for the same size fish, i.e. the same target field intensity as used in these calculations. The Im for backpacks was 1 amp whereas the Im used here was 5 amps. That was an arbitrary decision on my part to compare with the extent of the electrical field for spheres (69 cm) and Wisconsin rings (about 90 cm) when the same 5 amps at match was applied to a single anode or to an array of droppers. The shapes of the electrical fields differ based on the geometry of the electrodes. I’ll say more about that in the last blog of this series.

The question of the 5 amps at match arises again. That was an arbitrary decision. How valid is it? Unfortunately, I lack sufficient fishing threshold data using rectangular pulses of an “effective” waveform to test this assumption. I do have some data from a Louisiana Department of Wildlife and Fisheries electrofishing boat configured for the boat hull as the cathode and a single prod pole as its anode. Field intensity measurements were made at Sibley Lake, Natchitoches Louisiana in March of 2017, and further fishing threshold testing was done at Cane River Lake at Natchitoches later in March of 2017. The prod pole was 28 cm (11 inches) diameter, and the R100 was 127 ohms. The pulsator was a Smith-Root GPP unit, so the pulse shape was rounded. It is known that fishing thresholds are higher for rounded versus rectangular pulses. There is a blog on pulse shapes at this site, Electrofishing.net. At Cane River Lake, the ambient conductivity was 500 μS/cm. Peak voltage was measured with an oscilloscope, and the peak current was measured with a voltage gradient probe connected to an oscilloscope. The fishing threshold at Cane River Lake was 392 volts and 15.4 amps. The GPP settings were 120 Hz at 20+ percent of range on the 500-volt range. The target field intensity at 500 μS/cm was 0.444 V/cm.

SA = (15.4 x 1,000,000)/(0.444 x 500) = 69,369 cm^{2} based on current __or__

SA = (392 x 10,000)/(0.444 x 127) = 69,518 cm2 based on voltage

The small difference in calculated surface area between the current and voltage equations above is due to some round-off error.

Figure 4. Prod pole in use by Louisiana Department of Wildlife and Fisheries biologists. The loop is out of the water to cross over some vegetation.

Figure 5. Demonstration of prod pole use for a photo. Note the shallow depth deployment of the loop.

From the field intensity profile, not presented here, the estimated distance, r, was 102 cm. The Im at Sibley Lake was estimated at 5.6 amps, and for Cane River Lake it was 5.8 amps. These values are not exactly 5 amps at match, and there are at least two reasons for that, besides the subjective judgment of what is threshold. Because the pulse shape was rounded instead of rectangular, the expected Im value could be 7 amps or more versus the 5 amps assumed for rectangular pulses. Also in play was the operation of the prod pole. It is typically held just beneath the water surface to attract or stun fish where the dipper can capture them in the net. Because they are used so near the water surface, there likely is a substantial boundary effect with the water surface, and the R100 and A100 values could change dramatically with depth as for the backpack operation in waters of different depth. Due to the surface boundary effect, the field probably is spread more radially from the loop and may provide enhanced fishing. Thus, the capture efficiency of a prod pole may be quite high, and that may lower the fishing threshold. The rounded waveform and the shallow loop operation could be affecting fishing threshold in opposite ways.

A lot has been presented in these last five blogs on electrical fields. I expect to write one more blog on fields to summarize what has been covered and to discuss some aspects as yet not covered.