Tech Note 1221 Detail

How does PASCO Capstone calculate the velocity and acceleration data from the position data from the motion sensors?

Affected Products:

UI-5400 Capstone Site License
UI-5401 Capstone Single User License

Problem/Symptom:
How does PASCO Capstone calculate the velocity and acceleration data from the position data from the motion sensors?

PASCO Solution:

For purposes of illustration, let’s say we have a set of data, (x1,y1), (x2,y2), (x3, y3), (x4,y4), ...

A “two-point” derivative (span = 2) would use consecutive points for evaluation. For instance, the derivative’s set of data would be:

Note that when we calculate the independent values of the derivative, we get the midpoints of the original data set. Suppose we sampled for one second at a sampling rate of 10 Hz; the data set would have independent values of 0.00, 0.10, 0.20, 0.30, ... , 0.90, 1.00. But the derivative would have independent values of 0.05, 0.15, 0.25,...,0.95. Putting the original data in a table’s 1st column and its derivative in the 2nd column, we would see that the data is staggered.

A “three-point” derivative (span=3) uses each point, but skips a point for evaluation. You can think of it as using the previous and next point for evaluation.

Note that when we calculate the independent values of the derivative, we get the independent data of the original data set (except for the first and last points). That is, for a sampling rate of 10 Hz, the derivative data set would have independent values of 0.10, 0.20, 0.30, ... 0.90. Putting the original data in a table’s 1st column and its derivative in the 2nd column, we would see that the data lines up, except the derivative has data missing at 0.0 and 1.0.

When using a motion sensor, the velocity is determined based on a three-point derivative of the recorded position data. Similarly, the acceleration is determined by a three-point derivative of the velocity data. This way, the data aligns nicely in the table.

Creation Date: 08/30/2013
Last Modified: 08/30/2013
Mod Summary: