My Dad showed me a simple, cool way of connecting technology (like smart phones) and simple devices (like a wrist-watch) with the inner working of nature (which is to say "physics") the other day. He said he got the idea when he noticed that the bubble in a bubble level "moved" when it was laying on the seat as he drove to Home Depot.

Turns out, his Android-based G1 has a sweet bubble level ("Bubble," developed by Ben Zibble: Go here.). I have a wrist-watch. With these two things, my Dad and I started calculating the speed of all sorts of things we were riding in as we went from a rest state (in other words, stopped) to some state of motion. You can see the tools we used in the pictures below.

2) When the driver starts smoothly accelerating (science teachers will recognize the term "smoothly" here) start the sweep hand on the watch.

3) Note the average angle on the bubble level as you accelerate for some pre-set (and safe) time, say 15 seconds.

Now, ask the driver to note the speed of the car at the end of the pre-set time, but to keep quiet about it. Let's say the angle readout averaged 5 degrees, and that we accelerated for 15 seconds. How fast were we going?

Our terminal velocity, given constant (smooth) acceleration, is simply "acceleration multiplied by time." We can relate this to gravity, g, since we are using an inertial accelerometer. Here's our formula:

   v = at(sin(r)g) * t

where g = 32.2 fps/s

and r is 'bubble angle' after converting it from degrees to radians

To convert from degrees to radians: r = (Bubble Angle / 180) * pi, which is about 3.14. 

This gives you the following:

V = (sin( 5/180 * 3.14) * 15  = 42.1 feet per second at the end of 15 seconds. Converting to mph, v = 60/88 * 42.1, which is just under 30 mph. The conversion used is based on 60 mph being 88 feet per second, something my Dad learned from his Dad when he was 8.

Got your answer? Ask the driver how fast the car was going. The actual answer, in this case, should be about 30 mph. While it might make your friends wonder, the answer is NOT "minus 30" if they happen to live in the southern hemisphere. Gravity is pretty much the same everywhere on Earth. 

Ben's Bubble application uses the G1's internal accelerometer. Tilting your phone in a gravitational field is the equivalent of accelerating the phone in a car, train, or plane which tells you something about gravity and its effect on the world around you. This relationship is at the root of what Albert Einstein devoted his life's work to.

Here's the deal: The tilt angle displayed on the phone is derived from an internal set of accelerometers. When the G1's Bubble Level is held stationary, for example when you place it flat on a shelf, the only acceleration acting on the level is due to gravity. If the shelf is level, the bubble sits in the middle. As you tilt the level, the accelerometer responds to its changing orientation by sensing the relative force (in this case, direction -- force is a vector) of gravity as it is exerted along the individual x, y, and z axes of the accelerometer. Say what?

Picture three tubes, each containing two springs like what you'd find in a pen and a marble inside, with the marble between the ends of two opposing springs. One tube is mounted vertically (the z direction), and the other two are mounted horizontally, with one oriented right-left (call this "y") and the other forward/backward (call this one "x"). Sitting on the shelf, the right/left and forward/backward marbles are in the middle of their respective tubes between the opposing spring since there is no net force acting to expand or compress one spring or the other. But what about the vertical tube? Because the marble has mass, the bottom spring will be compressed by the marble while top spring is able to stretch out. The force causing the compression/extension is ... gravity! Thus, the accelerometer can detect which way it's is oriented.

Now, if the accelerometer is titled up until until it is vertical, the "front" spring will progressively stretch and the "back" spring will compress in the same way as the up/down springs had been, just as the springs in your seat are compressed as your arms are stretched away from the steering wheel when you accelerate rapidly in a car. In this analogy, you are the marble. Always remember: Sharp marbles wear seat belts.

The same thing happens with G1 Bubble Level if the phone, while still held flat, is accelerated in a forward direction: The "front" accelerometer relaxes while the "back" one compresses. Acceleration is acceleration, whether due to gravity or your foot on a gas pedal. F = ma. ;-)