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How to Calibrate Homemade Accelerometers

Your cellphone, your camera, the airbag in your car --- all have accelerometers. Accelerometers have been around for a long time, but it's only since the advent of microelectromechanical systems (MEMS) that they've become attached to mundane devices. And it's a good thing they have, because they convert changes in motion to electrical signals in applications for safety, fun, and function. But an accelerometer is of no use if you don't know how to translate its electronic output into a measurement of acceleration. That's what a calibration procedure is for.

Things You'll Need

Air hockey table and puck or carpeted board and plastic furniture sliders
String
Small pulley
Signal wires
Weights
Balance (weighing scale)
Signal recorder
Double-sided tape or rubber cement
Accelerometer
Spreadsheet program, or equivalent.

Instructions

- 1
  Attach the accelerometer to the air hockey puck. Use double-sided tape or rubber cement, or another temporary attachment method. Weigh the completed assembly and record the reading. If using a carpeted board instead of an air hockey table, attach the accelerometer to a small plastic floor protector --- the kind put under heavy furniture legs. For purposes of illustration, assume the mass of your completed assembly is 60 g.
- 2
  Attach one end of the string to the air hockey puck or furniture slider. Place the string so that it lines up with one axis of the accelerometer.
- 3
  Connect signal wires to the accelerometer and to the signal recorder.
- 4
  Put the hockey puck at one edge of the air hockey table or carpeted board, and cut the string so it is long enough to hang over the opposite edge of the furthest side of the table or board. Place the pulley at that edge of the table and route the string over the pulley.
- 5
  Hold the hockey puck or furniture slider while attaching a weight to the string. If using an air hockey table, turn it on. Let go of the hockey puck or furniture slider. Walk next to the table, carrying the wires so they don't influence the motion of the accelerometer. For purposes of illustration, assume your weight is 200 g.
- 6
  Calculate the acceleration. The force is supplied by the falling weight, and is equal to m1 multiplied by g in the downward direction, where m1 is the mass of the weight on the string, and g is the acceleration due to gravity, 9.8 m/s^2. The force accelerates the entire connected mass, which is the mass of the puck, m2, and the weight on the string, m1, so the final acceleration is given by:
  
  a = (m1/(m1 + m2)) x g.
  
  For the example problem, the acceleration is
  
  a = (200/(200 +60)) x 9.8 m/s^2 = 7.5 m/s^2.
- 7
  Let the puck get started, then record the reading from the accelerometer before the puck hits the opposite side or the weight hits the floor. Repeat the measurement with the same weight several times. Record the average output from your accelerometer. For this example, assume the average was 445 millivolts.
- 8
  Repeat the measurements of Steps 4, 5, and 6 using two or three additional weights. For example, assume you used weights of 100, 300, and 500 g, and measured readings of 370, 480, and 515 mV. The accelerations for the masses of 100, 300, and 500 g are 6.1, 8.2, and 8.8 m/s squared.
- 9
  Calculate the calibration equation for your accelerometer. You are looking for an equation that is of the form: output = scale x acceleration + offset. You can run a linear regression analysis by hand, with a spreadsheet program, or with a dedicated data analysis program. The regression analysis program is more accurate than an equation based solely on a couple of the data points you've collected. The data from this example results in an equation of acceleration = 0.018 m/sec^2/mV x output - 0.58 m/s^2. This calibration equation allows you to convert from accelerometer output to acceleration.

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