# Roller Coaster Analysis

Started by January 27, 2011
```Hi everyone.

I'm looking to see if anyone would be kind enough to help me out with a few
basic questions I'm looking for answers for.

Part of my job involves the analysis of the accelerations that are
experienced by passengers on roller coasters. This involves fixing
accelerometers to rides and analysing the data that they produce. I'm
required to post process the data with " a 4-pole, single pass, Butterworth
low pass filter using a corner frequency (Fc) of 5 Hz". I am sampling my
data at 150 Hz and I am not interested in any acceleration peaks that are
less than 200 ms in duration.

Could anyone please explain what a Butterworth filter is in laymans terms
and why it is needed in this scenario?

message and I will get back to you as soon as possible.

Thank you very much

```
```On 01/27/2011 11:29 AM, RideAnalyser wrote:
> Hi everyone.
>
> I'm looking to see if anyone would be kind enough to help me out with a few
> basic questions I'm looking for answers for.
>
> Part of my job involves the analysis of the accelerations that are
> experienced by passengers on roller coasters. This involves fixing
> accelerometers to rides and analysing the data that they produce. I'm
> required to post process the data with " a 4-pole, single pass, Butterworth
> low pass filter using a corner frequency (Fc) of 5 Hz". I am sampling my
> data at 150 Hz and I am not interested in any acceleration peaks that are
> less than 200 ms in duration.
>
> Could anyone please explain what a Butterworth filter is in laymans terms
> and why it is needed in this scenario?
>
> message and I will get back to you as soon as possible.

I'm not sure if you need to know what a Butterworth filter is, or if you
need to have a better understanding of what a low pass filter is.  A
Butterworth filter is a specific kind of filter, specified in the
frequency domain, that is as close to flat in the passband as possible.
So if you were to plot it's amplitude response vs. frequency, it would
have the closest thing to a straight line response starting at f = 0 and
going out.

The reason you need a _low pass_ filter in this scenario is because when
you measure your acceleration you'll be measuring a whole lot of sharp
(i.e. fast) accelerations.  These sharp accelerations can be quite
large, but because of the way that our bodies are put together, they
aren't as harmful to people as accelerations that last longer.  The low
pass filter reduces the effect of these sharp accelerations, while
keeping the effect of the accelerations that likely do cause harm.

The reason that a Butterworth, and that specific Butterworth, filter is
used, is for two reasons: one, at some point in the past some researcher
or industry group decided that it made a pretty good model for assessing
what accelerations are going to be harmful, and two, the same or another
researcher or industry group decided that it would be easy to reproduce.
Since one of the points of measurement standards is to make the
results unambiguous, and since "everyone" knows what a Butterworth
filter is, that's what was chosen.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html
```