The Mapping Lab

1. Measurement System:
   1. Anchor point
      • On one lengthwise side of tank, choose a point (0,0) in the tank at which the center of the fish will be. The fish will be located at the center of the width. You will use this Anchor point to correctly position the grid, the X, and Y markers and the suspension apparatus.
   2. Plexiglas grid:
      • On a piece of Plexiglas, mark off an x and y-axis so that (0,0) is at the center of the glass with a wax pencil or permanent marker.
      • Mark off lines every 2 cm in each direction as far as will be measured.
      • Place the grid on the bottom of the tank.
   3. For the x coordinates:
      • On masking tape, mark off a center point, and then mark off 2 cm increments in the positive and negative direction for the length that will be measured (the length of the grid).
      • Place the strip of tape along the length of the tank, SO THAT X=0 CORRESPONDS WITH YOUR ANCHOR POINT (0,0).
      • Put an identical piece of tape on each side where measurements will be taken.
   4. For the y coordinates:
      • On masking tape, mark off a center point and 2 cm increments in the positive and negative direction for the length that will be measured.
      • Place each end of the tape on one side of the tank so that the tape extends across the width of the tank. Make sure that the tape is slightly outside of where all measurements will be taken. Also, the center point of the tape should be directly above the x axis of the plexiglass grid.
      • Put an identical piece of tape on each side where measurements will be taken.
   5. String
      • Use two pieces of string, slightly longer than the length and width of the area being measured. The strings will be used to mark the point being measured (description in procedure)
2. Electrode Setup
   1. Creating the electrode
      • Wind two insulated wires and run them down the length of a thin wooden skewer.
      • Strip the end of each wire that will be in the water (only strip a small portion of each wire). Make sure stripped portions begin beyond the end of the skewer.
      • Separate the stripped ends of the wires so that they are about 1 cm apart.
      • Mark the skewer at the point that is level with the water line when the stripped points of the electrode are level with the mid-line of the fish.
   2. Connection to coaxial wire
      • Strip the ends of the wires that are not going into the water.
      • Solder one of the stripped ends to the ground (outer) wire within the coaxial wire (have your teacher demonstrate). This wire will now be the ground wire.
      • Solder the live wire (the one inside the clear plastic inner tube of the Coaxial wire) to the live electrode wire, making sure that the two wires running from the electrode do not touch.
      • Insulate the two bare connections from each other with electrical tape.
   3. Grounding the tank
      • Grounding minimizes the 60 cycle hum), use one insulated wire stripped on both ends. Place one end into the water, and connect the other end to the oscilloscope (there should be a specific ground screw on the oscilloscope, ask your teacher for directions).
        *Note: all tanks that are grounded should be connected to the same distinct ground. More than one ground will create a ground loop.
   4. Restraining the Fish (Follow picture diagrams.)
      • Make sure that the center of the fish is directly above the center point marked on the plexiglass grid and in line with the anchor point.
      • Let fish settle for ten to twenty minutes to ensure that the data is not altered as the fish adjusts to its surroundings.
      • Use a string to attach pantyhose restraint to the holding apparatus (see diagrams).

Procedure:

1. Turn on all necessary electronic equipment (oscilloscope, amplifier, and recording equipment)
2. Mapping Fish Alone (control)
   1. String setup
      • Mark the x-coordinate by attaching one end of the string to the x-value on the far edge of the tank and the other end to the same value on the near end of the tank.
      • Mark the y-coordinate by attaching one end of the string to the y-value on the left tape and the other end to the same value on the right tape.
   2. Measurements
      • Lower the electrode at the point at which the two strings intersect. Make sure the live wire of the electrode is directly below the intersection point at all times.
      • Measurements when neither x nor y = 0
        1. Place the electrode parallel to the x axis so that the ground wire of the electrode is farther away from the center point than the live wire.
        2. Place the electrode parallel to the y-axis so that the ground wire of the electrode is farther away from the center point than the live wire.
      • Measurements when y=0 ( it is necessary to take three vector measurements)
        1. x-vector: take one measurement so that the ground wire is along the x-axis further from the fish than the live wire.
        2. y-vector: take two measurements, both perpendicular to the x-axis, one with the ground wire closer to the far end of the tank, and one with the ground wore closer to the near end of the tank.
      • Measurements when x = 0
        1. x-vector: Take two measurements, both parallel to the x-axis, one with the ground wire closer to the right end of the tank, and one with the ground wire closer to the left end of the tank.
        2. y-vector: Take one measurement so that the ground wire is along the y-axis further from the fish than the live wire.
        3. Move the strings to the next x,y coordinates and repeat. repeat for every combination of x and y coordinates as marked off by the plexiglass.
3. Non-conductive Object
   1. Either suspend the glass rod from the top of the tank or attach it to a weight at the bottom so it extends from the bottom of the tank to next to the fish. The rod should be near the fish so that a distortion will be detectable.
   2. Repeat mapping fish alone step.
4. Conductive Object
   1. Follow same procedure as for non-conductive object, using metal rod instead of glass rod.
5. Recording Measurement
   1. On the oscilloscope, adjust the volts/cm knob and the time/div knob so that the entire amplitude fits on the screen.
   2. Adjust the distance from the top tip to the bottom tip in centimeters (the amplitude). We found a compass works well for this.
   3. Record the coordinate and its amplitude along with its amplitude along with a setting along with the setting on the volt/cm knob.

1. Find the x and y vector components for each coordinate
   • Multiply the amplitude by the setting of volts/ cm.
2. Find the magnitude of the resultant vector
   • When the coordinate is not x= 0 or y= 0
     1. Take the square root of the sum of the squares of the x and y vector components.
   • When x= 0
     1. Using vector addition (paying careful attention to signs of vectors) add y₁ and y₂. Use this vector as the y vector component and take the square root of the sum of the squares of the x and y vector components.
   • When y= 0
     1. Using vector addition (again paying attention to signs) add x₁ and x₂. Use this as the x- vector component and take the square root of the sum of the squares of the x and y vector components.
3. Find the angle of the resultant vector
   • Take the inverse tangent of the x vector component divided by the y vector component.
     *Note: it can be very useful and time saving to use a spreadsheet to make these calculations. Take the inverse tangent of the x vector component divided by the y vector component.
4. Contour graph
   • To see the results most clearly, graph everything on a contour graph, plot each r value on its x and y position coordinates.
   • Connect all like r values at specifics intervals (perhaps .2 or .5)
5. Visually comparing the different contour graphs
   • The effects of the conductive and nonconductive objects should clearly illustrated.