# Quickie: Which way does gravity point?

Everyone knows a compass always points north, and most people know it’s because of magnetic fields present on Earth’s surface.  There’s another force here on Earth directed to a central point, and that’s gravity.  Humans are quite adept at sensing gravity thanks to equilibrioception, where  fluid contained in structures in our inner ear provide feedback to help us stay balanced.

But machines, too, can detect gravity thanks to the simple accelerometer.  Already present in most smartphones today, accelerometers react to gravity with tiny springs, creating a voltage difference that we can measure and turn into meaningful units.

On Android, we can easily read the accelerometer data:

### Using accelerometers to emulate human’s perception of gravity

I’d like to show how we can use an Android phone (even my dusty old Droid Eris) to visualize the force of gravity.  To save time, we’re only going to use two dimensions, x and y, but the technique used here can easily be extended into 3D.

Let’s represent gravity the same way students in a high school physics class would — with an arrow pointing down.  The goal would be the ability to rotate the phone (changing the x and y position), while still having that arrow point down, illustrating the direction of gravity.

The first thing we’ll need to do is convert the rectangular coordinates given to us (x and y) to a polar system (r, θ), where extracting an angle is much easier.

Thinking back to high school geometry, the inverse tangent will provide that angle directly.  Java has a built-in method, atan2(), which even gracefully handles the divide-by-zero case when x = 0. Because the image rotation I’m using is based on degrees (more on that in a moment), we can convert the radian angle to a common degree (0-360°).

That gives us the degree rotation of the phone in 2D.  We’re almost there.  To determine the degree that we would like the gravity arrow to point, we need to offset that degree, modulo 360 to keep us within the range (0-360°):

Now it’s just a matter of re-drawing the arrow image on the screen.  Android offers some fancy animation techniques, but for this quickie project, I chose to use a matrix rotation:

With that code in place, we can finally visualize the force of gravity, at least in two dimensions:

This project was a quick one (writing this blog entry actually took longer than the code itself), but I think it’s important to show how we can figuratively “teach” a device a human trait and give them a new skill.  For instance, with a faster refresh rate and perhaps a little more accuracy, a robot can use this technique to keep itself balanced, much like humans use information from gravitational forces to stay balanced.

Github available here.

# Wind Turbine Analysis

For our final project for CS 59000: Embedded Systems, a partner and I implemented several tests on a small-scale wind turbine using the Texas Instruments MSP430 board. We use the Analog to Digital Converter (ADC) to gather information on voltage generated by the turbine and rotations per minute calculated with the help of an optical tachometer. We then send these values to a Java-based user interface to report in real-time on an attached computer.

For the final part of our project, we designed a wind turbine stand on springs that we can use, along with the MSP430, to measure accelerometer data from the wind turbine under stress. We also send the real-time data to the user interface on an attached computer.

### Findings

#### Power Coefficient (Cp)

We measured the following characteristics of the wind turbine at LOW fan speed:

• AT = 0.134614 m2
• V3 = (2.101 m/sec)3 = 9.275
• ρ = 1.2041 kg/m3 at 20°C (from Wikipedia)

The average voltage reported by our program at LOW fan speed was 2.304 volts. Resistance was set at 330 Ω.

Using these values, we found the power coefficient, Cp, to be:

Cp = 0.00929 or 0.01

#### Tip-Speed Ratio

This part of the project required the use of the optical tachometer connected to the MSP430 board. The tachometer will output a high value when no blade blocks the beam, and a low value (close to zero) when a blade is in front. We read this information and convert the rate at which blades are passing in the beam to compute a rotations per minute (RPM) value.

The average RPM we measured at a given time was: 55 RPM

We measured the radius of a blade, and found R = 20.7 cm or 0.207 meters.

At LOW fan speed, the velocity of wind was recorded as V = 2.101 m/sec * 60 s= 126.06 m/min.

Using these values, we found the Tip-Speed Ratio to be:
λ = .567 rotations

#### Accelerometer Data

We constructed a special stand for the wind turbine that allows the turbine and MSP board to move in unison, while still being flexible to allow natural movement due to the wind.

For this part of the project, we modified the provided Java program to also display accelerometer data in the X- and Y-axes. We track and record this data in real-time, which gives some insight into how the wind turbine is moving as the speed and direction of wind changes.

Although we are not able to give a unit for these values, the magnitude of change can indicate what is happening in the physical system. For instance, when we see X values change from near-zero to negative, we know that stress is being placed in the wind turbine in the negative X direction (see diagram below — blue values represent negative readings).