# Calculating Head Pan Angle with Accelerometer Measurements

• gunnerone
In summary, the author is trying to measure the angle of a user's head and roll, and is having difficulty due to the small accelerations that the device experiences.
gunnerone
Hi, please don't hesitate to reply to either of my paragraphs. Or ask for clarification. The first paragraph descibes the basic problem, and the second one is more indepth. I'd be happy if I could get just the first one working.

I'm working on a project were a two-axis accelerometer will be mounted to a helmet, and worn by a user. Currently I have the accelerometer mounted with both axes parallel to the earth. The problem I'm working on, is having the user pan their head(moving parallel to the earth), left or right, and calculating the angle. My approach is to calculate the distance in each direction(x and y), using d = d0 + V0*t + 1/2 * a * t^2, and then take the inverse tangent of these two results. Then store the new velocity, using v = v0 + a*t, for use in the next calculation. Does this sound like a good approach, or is there perhaps a better way to do it?

As it currently is, I can calculate the amount the user rolls or tilts their head, since the measured acceleration changes as the axes become more or less perpendicular/parallel to the earth. i.e. When the X-axis is perpendicular to the Earth it experiences +-1g of acceleration, when it is parallel it experiences 0g. So these values can be used directly. However this approach doesn't work for panning, since the movement is parallel to the earth. Ideally, I'd like to be able to calculate the amount the user pans their head even when their head is tilted and rolled. Any advice or ideas would be greatly appreciated.

Accelerometers don't work like that. Accelerometers are dynamic measurement devices. If you were to move your head slowly, you would not pick up any acceleration. This is due to the piezoelectric nature of the accelerometers.

What you need is something like an iclinometer.

Thanks for your reply. Could you please explain a little more? If I have a very sensitive accelerometer wouldn't I be able to measure the acceleration even if they pan their head slowly?

Also, the inclinometer doesn't look like it'll work for the panning, since it measures with respect to gravity.

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Accelerometers are dynamic measurement devices. The piezoelectric elements create a charge when deformed. However, that charge is quickly dissipated due to voltage leakage. For eample, they are good for cyclic vibrations that induce sinusoidal accelerations (a vibrating piece of machinery), but they do not work under a continuous acceleration (like gravity).

Honestly, I think that the accelerations are going to be so small that your measured signal is going to get lost in the usual noise of a system. However, it's easy enough to set up. Give it a go.

## 1. What is an accelerometer?

An accelerometer is a sensor that measures the acceleration of an object. It can detect changes in acceleration in three different directions: forward and backward, left and right, and up and down. It is commonly used in electronic devices such as smartphones, fitness trackers, and cars to measure movements and provide orientation data.

## 2. How do accelerometers work?

Accelerometers work by using the principles of Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration. Inside an accelerometer, there are tiny springs and masses that move when the device accelerates, and this movement is converted into an electrical signal that can be measured.

## 3. What are accelerometer calculations used for?

Accelerometer calculations are used to interpret the raw data collected by the accelerometer and convert it into meaningful measurements such as speed, distance, and orientation. These calculations are essential for applications that rely on accelerometer data, such as step counting, gesture recognition, and virtual reality.

## 4. How accurate are accelerometer calculations?

The accuracy of accelerometer calculations depends on various factors, such as the quality of the sensor, the calibration of the device, and the algorithms used to process the data. In general, modern accelerometers can provide accurate measurements within a few percentage points, making them suitable for many scientific and industrial applications.

## 5. Can accelerometers be used to measure gravity?

Yes, accelerometers can be used to measure gravity. Since the force of gravity on an object is constant, an accelerometer at rest will measure 1g (9.8 meters per second squared) in the direction of the Earth's gravitational pull. This can be used as a reference point for other measurements, such as detecting changes in elevation or determining the orientation of an object relative to the ground.

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