motion sensors

[Ari Hamalainen <aohamala@CC.HELSINKI.FI>]

Hello phys-l, and greetings from Helsinki.

Sorry about starting a new thread for the subject; I can not make a reply
to the original question. I have not been a member of phys-l for some
time, but Dan persuaded me to join again.

> 1. The new motion sensors (Pasco II) have both a wide and a narrow
> beam setting. When should one use which? So far, I have adopted the
> empirical approach: I tell my students to try both and use the one
> which seems to work best for them. A typical use is to measure a
> rolling cart on a 2-m Pasco track. Curiously, when I go around the
> room, I find about half the lab groups swear the narrow beam works
> better, and half say the same about the wide beam. Comments?

The narrow setting reduces possibility to get false echoes from objects to
the side of the track, but it also reduces the sensivity of the sensor,
requiring stronger echo, but again reducing the possibility to receive
"old" echoes that have been bouncing back and forth in the room. The
conditions for the lab groups surely are not exactly the same, so there
may well be disturbing factors that can be circumvented for some groups by
using the narrow setting, and for some groups by using the wide setting.

> 2. Dan emphasizes that "Advanced methods for calculating less noisy
> velocity and acceleration data from sonar position data yield better
> data at the expense of a higher student cognitive load and hence are
> not defaults in the software." I would like to hear if there is a way
> to change the defaults to the "advanced" methods and exactly what
> these are. I don't understand the concern about higher cognitive
> load, since I don't ask my students to check the finite-difference
> calculations. (No flames please. I know, I know: I should have the
> students compute these using a slide rule and draw the graphs by
> hand, right? :-) Presently, the only "advanced" operation I tell my
> students to try is to adjust the sampling rate and the averaging
> ("Points in Derivative/Tangent Calculations" in Logger Pro --
> incidentally, is there a way to average Force Sensor data?) again by
> trial and error.

Logger Pro calculates velocity and acceleration with its Derivative
function. There are also Smoothderivative and Smoothsecondderivative
functions, which give slightly different results. The explanation for how
they work can best be found in the LoggerPro Help, topic is Calculating
derivatives. The value in "Points in Derivative/Tangent Calculations"
affects how much smoothing takes place.

Logger Pro has a method for smoothing any measured or calculated data
column, not only derivatives. Let's say you are measuring force, and would
like to reduce some noise from the data. For that, you must create a new
data column for the smoothed force data. From the menu, select Data - New
Column - Formula. In the Options tab, input the labels (say, Long Name =
ForceSmooth, Short Name = Fs, Units = N). In the Definition tab, input the
Equation for the new column. First, select the desired smooth() function
from the Functions list, then data column Force from the Variables list.
The Equation becomes smooth("Force"). When you click OK, ForceSmooth
becomes a new data column that can be plotted etc. like any other. The
magnitude of the smoothing effect can be adjusted by varying the "Points
in Data Smoothing Calculations" in Experiment - Options. Exacthy HOW the
Logger Pre calculates the smoothing is not clear (it does not seem to be a
simple moving average).

It also possible to combine the methods, that is, to smooth data first and
then calculate velocity & acceleration, or calculate velocity and / or
acceletation data first and then smooth them. The tradeoff always is that
the more you smooth, the more you lose rapid alterations.

Pasco's Data Studio offers basically similar possibilities.

These "local" methods for smoothing and calculating the derivatives work
in real time, that is, during the measurement. There are other more or
less "global" methods that require the full data column to be available.
This means fitting a curve to a region or the full set of data.

Let's say we have recorded the position of a weight hanging on a spring.
The result resembles a sine curve, but there is (in this fictious case)
enough noise to cause the velocity and acceleration data to be too ugly.
In Logger Pro, we may fit a sine curve to the data, and create a new data
column as a result. If we then calculate and graph the first and second
derivatives of this "idealized" position data, the results are of course
very clean.

There is at least one MBL sofware (CoachLab 5 from The Coach Team,
CMA/Amstel Instituut, University of Amsterdam - see
http://www.cma.science.uva.nl/english/index.html) that allows even more
sophisticated global smoothing by spline and Bezier approximation.

> 3. Dan recommends adding a "sail" or "flag" reflector to the carts to
> improve return signals. I'm a bit worried about air drag - how large
> a flag is optimal?

I use 5 x 6 cm flat acrylic reflectors, and have never noticed effects
that might have caused by air drag. Have not tried the corner reflectors
that Scott Goelzer recommends; maybe I should.

> 4. Another recommendation is to avoid tennis balls because they are
> fuzzy. Indeed, a simple experiment I do early on is have the students
> drop a tennis ball onto a motion sensor to determine g and students
> often have trouble getting good data. But smoother balls are usually
> harder - do folks protect their sensors from impacts? We often use a
> grille on a frame boxing the sensor but I suspect these introduce
> some noise. (Or students can catch the ball at the last minute but
> they are often not coordinated to do this without disturbing the beam
> earlier.)

George Spagna already answered this: reverse the setup. Point the sensor
down and hang it high, ca. 2 m above the floor, and well away from the
desk edge. (We use a table clamp, two rods attached end-to-end, and a
third horizontal rod to which the sensor is attached. An extension cord
for the sensor may also be needed.)  This setup has the additional
advantage that one is able to record data of several bounces. One also
immediately sees the important but non-intuitive fact that the
acceleration of the bouncing ball does not depend on whether the ball is
going up or down. We use volleyballs, small basketballs, soccer balls,
superballs and even golf balls.

--
Ari Hamalainen   lecturer, Department of Physical Sciences
tel +358 (0)9 19150654 (desk), +358 (0)40 5143867 (mobile)
fax +358 (0)9 19150662
Ari.Hamalainen@Helsinki.fi, http://www.helsinki.fi/~aohamala/