Building an accelerometer can be very difficult; accuracy and practicality are big issues. The simplest of devices consist of a clear tube with two rubber bands in it attached to a weight. The issue with this however is accuracy; a rubber band stretches very easily and because your average rubber bands have fairly high spring constants and therefore require large masses to be able to see any acceleration (upwards of 200 grams). These are nice however to take to an amusement park and measure the g's being pulled on different rides.

The construction of this first, very basic design which can be made from household items, is as follows:

*Materials:* tennis ball tube or paper towel tube or clear pvc piping, two rubber bands, scissors, a bolt (heavy enough to stretch the rubber bands when hung), duct tape, two paper clips.

*Instructions:*

- If you're not using a clear tube, cut a slit in the side of the tube so that you can see the device.

- Cut the rubber bands into strands and tie one end of each band to the bolt or other weight.

- Fasten the ends of the rubber bands (with the bolt at the center) to the ends of the tube; the bands should be just barely loose so that the bolt can move around in the tube.

*Calibration:* With the device in a vertical position, mark where on the tube the bolt comes down to: this mark is one g (9.81m/s^2). You can then flip it over and make a negative one g mark on the other side. Halfway between these two marks will be the zero g mark (which should be where the bolt is when the device is held horizontally), and multiple g marks can be measured out based on negative one and one. To be more accurate, hang multiple bolts of the same weight onto the current weight: 2 weights = 2g's, 3 weights = 3g's and so on.

*Use:* This device can be taken in a car, on an amusement park ride or anything where you'll experience acceleration. A more accurate accelerometer is, however, described below.

A spring-mass system is just that, a mass on a spring. This is the next best thing to use for an accelerometer if you have the patience to build it and time to calibrate it. So, here it goes:

*Theoretical Explanation:* When accelerated, the force of the acceleration will stretch out the spring due to the mass, giving the device a different reading. Because of Newton’s Second Law, F = ma which can be transformed into a = F / m, the acceleration of the device as a whole is proportional to the force exerted on the spring and inversely so to the mass attached to the spring. In addition, because the distance the spring extends is known by the equation F = kx as x, with a known spring constant k, each displacement value can be attributed to a certain acceleration value based on the following proof…

F = m * a

F = k * x

m * a = k * x

a = (k * x) / m

This produces a linear correlation between acceleration and displacement based on a given mass and spring as a result of Newton’s Second Law. The use and application of this correlation is explained in detail further below. The method of reading accelerations can be a paper clip, laser pointer, or other pointing device attached to the cart/weight pointing down to a scale running next to the track.

*Materials:*9 inch 2x4 piece of wood (or any length really), model train track (9 inches), un-built model train kit, a small plastic box (1 cubic inch approximately-- must fit on train wheels), two C-115 Century Corp Springs (at your local hardware store), poker chips (or some other form of weight which is incremental) two paper clips, power tools, glue (epoxy).

*Instructions:*

- Glue the train track down the length of the piece of wood.
- Drill holes into each of the ends of the piece of wood so that a paper clip can be put on each end so that each spring can attach to the paper clip with falling off, I recommend a V-shape bent into the paper clip.
- Glue the paper clips to the wood in the holes.
- This next part involves the construction of a cart...
- Take either one or two train wheels and glue the plastic box to their top; be careful not to glue the wheels and to make sure the wheels are aligned if you use two wheels.
- The cart can now be placed on the track and be able to freely run up and down with little friction.
- Each spring should attach to either end of the cart and then to their respective paper clips.
- Weight can now be added to the cart for more sensitivity.
- You will notice that cart settles down to the same position on the track every time given that the connection points of the springs don't move.

*Calibration:* Experimental data may be attained by tipping the device at readings multiple of one centimeter. The angle can then be recorded at each point and trig functions should be used to solve for the component of gravity pulling the box down the track at each respective measurement. Different masses on ones cart can be used to allow for a wide range of acceleration while maintaining accuracy by calculating the correlation for each of the 3 sets of data values. Spring constants should be attained using the following equations and the known values, for each data pair...

F = m * a

F = k * x

m * a = k * x

k = (m * a) / x

The averages for the spring constants of each data set should be calculated. Using this value as k in the known equations...

F = m * a

F = k * x

m * a = k * x

a = (k * x) / m

...a calibration equation can then be determined for each data set using displacement (x) as the independent variable and acceleration (a) as the dependent variable. The device can now be used in multiple modes each with different acceleration ranges, also to be calculated based on the maximum and minimum displacement values along with the known displacement/distance coefficient. A calibration chart/table for the spring C-115 is on the node C-115. The information on this page was compiled and calculated completely by me. I do not claim 100% accuracy considering a regression equation was used, it is however at least 95% accurate if not better.

I left a good amount of description out and wasn't highly specific in the construction to allow for you to make the accelerometer how you wish, the concept is fairly simple... Wouldn't want to make it too easy. Message me with any questions or concerns you have, happy building!