accelerometer scale factor elementary question

[kievari]

Hi,
I've received a new accelerometer with a scale factor declared as: 800 mV/g @ 1.5g. I googled and searched the forum but still can't fully be sure I understand the accelerometer and its functioning, so please correct me where I'm wrong:

One thing that very helped me to get some understanding, was this post:
MAV-blog : Accelerometer to pitch and roll
where you see this:

giving the calculation of:
accelerometer = cos (theta) * gravity
theta = acos (accelerometer / gravity)

Formula is easy and beautiful, and this is my first question please:
what 'gravity' means there? Suppose the robot owning this accelerometer is on Earth surface, then this 'gravity' means 9.8m/s^2?

Next how to relate this to my accelerometer board output please?
I apply a 5V to its board and it has a 10bit ADC, so if I receive:
x(LSB) * 5(V)/1024(LSB)
now to get rid of V dimension I use the scale factor:
x(LSB) * 5(V)/1024(LSB) * (1/{800mV/g})
get rid of 'm':
x(LSB) * 5(V)/1024(LSB) * (1000/{800V/g})
or
x(LSB) * 5(V)/1024(LSB) * (10/{8V/g})
finally:
x*(25/4096)g

questions:
1. but this finall scale factor is a very small number! seems wrong
2. in data sheet the scale factor is declared: 800 mV/g @ 1.5g
how to take to account the 1.5g? I can imagine when the vertical upward is 1g and vertical downward is -1g, but can't imagine 1.5g.
3. Am I right with the g unit there? As long as I know, this is an embedded number like 9.8m/s^2 on Earth surface. So finally, having 'g' in both accelerometer and gravity in this formula:
theta = acos (accelerometer / gravity)
we remain with a scalar number and everything stands good at the end of the story, correct?!

Please help to make this clear!

 

[mdUJ]

Hi,

it´s quite easy to calculate the acceleration for every axis. Put your accelerometer flat on the table.
It will output the bias values for X- and Y-axis (acc_x_bias). If you are using a 3-axis accelerometer, then the Z-axis will output the value for -1g.

Now rotate the a accelerometer 90 degrees X-axis up. You get the +1g value (acc_x_1g) for the X-axis. Do this for every axis.

With these calculations you get the acceleration in g and finally the angle in degrees.

sf_x = 9.80666 / (acc_x_1g - acc_x_bias); // Calculate the scale factor for X-axis
acc_x = sf_x * (adc_x_reading - acc_x_bias); // Calculate the actual acceleration of X-axis
angle_x = asin(acc_x / 9.80666) * 180.0 / PI;

Be aware that a calibration routine for high performance devices are much more complex, but for simple applications this should fit.

Regards

Udo

 

[FvM]

Your calculation assumes, that the acceleromter output would be fed to a 5V/10-Bit ADC without additional amplification. You correctly calculated an LSB of
0.0061 g respectively about 1/164 g. You would get a fourfold sensitivity by applying a gain of four before digitizing the measurement.

but can't imagine 1.5g

Drive a roller coaster, you'll imagine after that.

 

[mdUJ]

Hello FvM,

Where do you see values like "5V" or the resolution of a "10-bit ADC" in the calculation?
That´s the nice thing of this way to calculate the acceleration.
It works even without knowing the sensivity (+-mV/g), the full scale (+-x.xg) of the accelerometer, the ADC resolution and supply voltage.

Sorry, but I cannot follow your objection...

Regards

Udo

 

[FvM]

It's not in your calculation. When using a 10-Bit ADC, as said in the original post, quantization shouldn't be ignored.