Using accelerometer data to calculate distance

[JacobTV]

I am looking for some help, or even advice as how to proceed.

I am trying to quantify an impulse from a hand (a high velocity low amplitude motion). In attempt to do that, I've tried attaching an accelerometer to my hand.
My problem is, that the values I'd like to calculate as an objective measure of the quality of the motion is speed and distance.
Here is one example of some of the data:

Date, t, Acceleration X (g), Acceleration Y (g), Acceleration Z (g), Acceleration Scalar (g), Speed (m/2)
2015-11-19 07:57:01 +0000, 43.609411, 0.382812, 0.359375, -0.875000, 0.020451, 1.589126
2015-11-19 07:57:01 +0000, 43.655306, 0.367188, 0.414062, -0.855469, 0.018872, 1.589993
2015-11-19 07:57:01 +0000, 43.699334, 2.187500, 0.417969, -1.816406, 1.873880, 1.672496
2015-11-19 07:57:01 +0000, 43.759296, 0.632812, -0.160156, -1.070312, 0.253663, 1.687706
2015-11-19 07:57:01 +0000, 43.804159, -1.003906, -0.941406, -0.929688, 0.660841, 1.717353
2015-11-19 07:57:01 +0000, 43.851403, 0.078125, 0.781250, -0.699219, 0.051362, 1.719780

The calculations I've attempted with this data is as follows:

t0=43,655306
t1=43,759296
dt=0,10399
g=1,87388
a= g*9,815=18,3921322 m/s²
s=(a/6)*dt³=0,003447113 m

I am assuming that distance is a second integral of acceleration

From this I get that the distance of the motion is 3,4mm which sounds implausible.

Is there another way to calculate or use the accelerometer to get the data I need?

I hope you can help?
Jacob

 

[sophiecentaur]

Hi
Looking at your table, the scalar acceleration would be √ (A_x²+A_y²+A_z²) (?)
The result (in the table) should be greater than any of the individual components but it doesn't seem to be. What is that "scalar"?
What would you expect the speed to be, after 0.1s? Those SUVAT equations tell you s = ut + at²/2 for constant acceleration. What does that give you? That answer is 'reliable' so compare it with what you got. Compare the SUVAT equation with yours. It looks like you've done one too many integrations for your data. I think you are thinking in terms of Δa to give you your answer but then you should also include the initial acceleration value (which is what SUVAT does) But, of course, you would be aiming at doing all this in 3D so check the 1D answer first.

 

[cosmik debris]

You will probably get a lot of noise in your calculation using integration to find velocity and distance, a better way is to do an FFT and do the calculations in the frequency domain.

http://blog.prosig.com/2010/12/16/m...tween-acceleration-velocity-and-displacement/

 

[sophiecentaur]

You will probably get a lot of noise in your calculation using integration to find velocity and distance, a better way is to do an FFT and do the calculations in the frequency domain.

http://blog.prosig.com/2010/12/16/m...tween-acceleration-velocity-and-displacement/

Definitely the better approach but a bit of a dark art for a beginner. To reduce noise effects it is often convenient to do a low pass filter ( average over a number of samples of acceleration)

 

[A.T.]

s=(a/6)*dt³

I am assuming that distance is a second integral of acceleration

That does't look like the second integral. See:
http://hyperphysics.phy-astr.gsu.edu/hbase/acons.html