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How to Find the Gradient of a River

River gradient measures how many feet that body of water descends over a given distance. The higher the gradient, the steeper (and usually faster) the river. Think of the near-vertical ramps for fast movement in skateboard parks compared to the gradually sloping wheelchair paths at the hospitals where skateboarders end up. You and a helper can find a river's gradient, using simple tools you build yourself and a bit of trigonometry.

Things You'll Need

  • Tape measure, 20 feet
  • Pencil
  • Protractor
  • Stick pen
  • 1 foot of string
  • Metal nut
  • Waterproof clear tape
  • Waterproof red tape
  • 2 wooden poles, 5 feet long
  • Notebook
  • Calculator
  • Trigonometry tables
  • Waders or rubber boots
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Instructions

  1. Build a Clinometer

    • 1

      Begin assembling the clinometer, which is used to calculate angles. Turn the protractor upside down so its straight side is on top. Tape the string with clear tape to the midpoint of the straight side so the string hangs down and can move freely.

    • 2

      Remove the cover and end cap from the stick pen. Unscrew counterclockwise and remove the ballpoint and ink stick. Using clear tape, attach the now-empty pen tube to the straight side of the protractor, forming the clinometer sight.

    • 3

      Tie the metal nut securely to the free end of the string.

    Build the Survey Poles

    • 4

      Measure off 12 inches from the end of one wooden pole and mark the spot with a pencil. Measure an additional 12 inches from that spot and mark it.

    • 5

      Cover the 12-inch section of pole that you marked off, using the red tape.

    • 6

      Measure off an additional 12 inches, make a mark, go down the pole 12 inches more and make a mark. Using the red tape, cover this second 12-inch section of pole that you marked off, leaving a 12-inch gap between taped sections.

    • 7

      Measure, mark off and tape the second wooden pole the same way.

    Measure the River Gradient

    • 8

      Place a wooden pole vertically in the river so it rests on the bottom.

    • 9

      Hold the tab of the tape measure against the pole. Have your helper walk off 20 feet upstream with the tape measure. Place the second wooden pole vertically in the river at that spot.

    • 10

      Hold your clinometer against the top of the first red section on your wooden pole so the sighting tube is on top and at a right angle to the pole, and the string and weight hang down but turn freely. Face your helper.

    • 11

      Looking through the sighting tube, turn the protractor until you line up the tube with the top of the first red section on your helper's wooden pole. Press the string carefully against the protractor and note the angle. Record the reading in your notebook.

    • 12

      Move to where your helper is standing. Grasp his wooden pole without moving it, and hand your pole to the helper so he can move farther upstream. Repeat Steps 2 through 4 and again record your findings.

    Do the Math

    • 13

      Average out the findings, in degrees, that you've recorded in your notebook. For example, your angle finding is 5 degrees.

    • 14

      Look up the tangent of 5 degrees, using a tangent table such as the one at Science-Projects.com. Write down the figure, 0.0875. Multiply that figure by 20, the number of feet between the poles when you made the measurements. Write down the result, 1.75.

    • 15

      Multiply your result by 264, the number of 20-foot sections in a mile, to determine the river's gradient. Rounded off, the result is the gradient for a river that rises 462 feet per mile as you move upstream.


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