Solving an Integration Error with Acceleration Data

  • Thread starter Thread starter mark2468
  • Start date Start date
  • Tags Tags
    Error Integration
AI Thread Summary
The discussion centers around an integration error in calculating distance from acceleration data, where the expected distance should return to zero but does not. The user, Mark, integrates acceleration data but receives incorrect velocity and distance values, prompting questions about the method used. Participants suggest including time intervals, which are 0.333 seconds, and emphasize the importance of calculating displacement using average velocity. They recommend using the formula for displacement based on initial and final velocities during each time interval. The conversation highlights the need for accurate integration techniques to resolve the discrepancies in the distance calculation.
mark2468
Messages
12
Reaction score
0
Hi.

I have a set of data representing acceleration. To get the distance I integrate twice using a summation method and looks like:

accelleration: 0, 40, 30, -50,-80, -40.
velocity: 0, 40, 70, 20, -60, -100.
distance: 0, 40, 110, 130, 70, -30.

The distance should be zero as the movement goes back to the original point so there clearly is an error. Is there a better way to get the distance. I have heard runge kutta is good for this sort of stuff but am not sure where and how to put the data in. Any suggestions to how i can sort out this error.

Thanks.

Mark.
 
Physics news on Phys.org
mark2468 said:
Hi.

I have a set of data representing acceleration. To get the distance I integrate twice using a summation method and looks like:

accelleration: 0, 40, 30, -50,-80, -40.
velocity: 0, 40, 70, 20, -60, -100.
distance: 0, 40, 110, 130, 70, -30.

The distance should be zero as the movement goes back to the original point so there clearly is an error. Is there a better way to get the distance. I have heard runge kutta is good for this sort of stuff but am not sure where and how to put the data in. Any suggestions to how i can sort out this error.

Thanks.

Mark.

Can you include time information in your dataset? What are the time intervals?
 
time intervals are 0.333 seconds.
 
mark2468 said:
time intervals are 0.333 seconds.

If your acceleration is 40m/s^2 for 1/3 of a second, you are not going 40m/s at the end of that time interval...
 
mark2468 said:
time intervals are 0.333 seconds.
And is the acceleration in units per second^2? If so, haven't you got the wrong values for velocity, as the time intervals were less than a second?

EDIT: missed berkeman's post, sorry
 
Apart from the length of the time interval, the displacement during a time interval Δt is the average velocity multiplied by Δt. In the first interval it is 20 (Δt)2, and the total displacement is the sum of all the individual displacements.

ehild
 
So what is the best way to synchronise them. Is there a formula or just divide by that ammout. e.g. 40/3, 30/3 etc or whatever the sample interval is. Any links with examples of this available?

Thanks again.
 
Assuming constant acceleration during a time interval Δt, the displacement during Δt is

d=(v(initial)+v(final))/2 *Δt.

ehild
 
Back
Top