The Physics Lab 1 post described a first experiment using ultrasonic rangefinders.  The students have not really done the Wikipedia-style writeup of how an ultrasonic rangefinder works that I wanted.  I’m not sure whether to push for that or to let it slide—it is important to develop technical reading and writing skills, but they have not yet gotten to the point in the physics course where they could actually derive the speed of sound equation.  The speed of sound in a gas is only vaguely referred to in Chapter 12 of Matter and Interactions, though there is quite a bit on the speed of sound in a solid.

I ended up buying two different ultrasonic rangefinders:

• PING))) ultrasonic range finder(Note: parallax.com also has mounting brackets, servo-mount option for panning, and packages that combine the range finder with other sensors.)
  

  Parallax PING))) sensor

• MaxBotix LV-MaxSonar-EZ2 MB1020
  
  

  MaxBotix rangefinder

Both of these rangefinders provide a pulse-width output that can be measured with the Arduino pulseIn function call.  The measurement is provided in microseconds, but seems to have a slightly coarser resolution, with measurements spaced about 5 microseconds apart.  To convert round-trip time into round-trip distance, we have to multiply the time in seconds by the speed of sound in meters/second.

There is an online calculator for the speed of sound as a function of temperature, pressure, and humidity, which gives a citation for the calculation (from the Journal of the Acoustical Society of America), but does not give a clear statement of calculation actually used.  The same calculator (at least citing the same source) is also available from UK’s National Physical Lab.  I used a simpler approximation (without humidity or pressure corrections) from Wikipedia’s Speed of Sound article:

On Friday, we did the lab itself:

1. Hook up the rangefinder to the Arduino and program the Arduino to keep taking measurements and reporting them to the serial line. (I wrote the Arduino program myself, but my son is working on a Python program to record a series of measurements from the Arduino, which will be needed for the next lab.)

   

   The setup for Lab 1. The Ping sensor is plugged directly into the Arduino, which sits on top of a copy of the OED, to get it far enough from the floor that we don't detect the floor rather than the wall.

2. Calibrate the sensor by placing it at carefully measured distances from a hard wall and recording the readings.  Repeat at several different distances.  (Record temperature, humidity, and barometric pressure, if possible.)  Here are the measurements made by the students, taking just the midpoint of the range observed:

# MaxBotix LV-MaxSonar-EZ Calibration
# Distance (centimeters)    Delay Time (microseconds)
10                818
20                1075
30                1515
40                2299
50                2887
60                3470
70                4060
80                4645
90                5231
100               5815

# Parallax Ping))) Sensor Calibration
# Distance (centimeters)    Delay Time (microseconds)
10                735
20                1215
30                1800
40                2405
50                3015

They had a lot of trouble getting consistent readings for the Ping))) sensor.  I think that this may have been due to trying to take the measurements without pausing enough between them, so I added an extra millisecond delay after each Ping))) measurement, and my son and I collected new data today.  We modified the setup slightly, so that instead of using a tape measure on the floor, we measured from the wall to the front of the Ping))) sensor with a steel tape measure.  Here are the measurements we made:

# Ping))) calibration data
# 1 October 2011
# Arduino report several (usually 6) measurements for each distance
# We recorded the actual distance, the minimum and maximum reported time of flight,
# and the minimum and maximum distance reported by the Arduino.
# The reported distance assumed 343.21m/sec speed of sound, and that the time of flight
# was twice the distance.
#distance(cm)  min_tof(usec) max_tof(usec) min_cm max_cm
10    616    624    10.57    10.71
20    1225    1230    21.02    21.11
30    1786    1818    30.65    31.20
40    2385    2391    40.93    41.03
50    2939    2962    50.44    50.83
60    3540    3542    60.75    60.78
70    4065    4089    69.76    70.17
80    4610    4729    79.11    81.15
90    5240    5265    89.92    90.35
100    5833    5858    100.10    100.53
110    6444    6446    110.58    110.62
120    7018    7050    120.43    120.98
130    7575    7582    129.99    130.11

These measurements were fairly consistent (though the variation is larger than I’d like).  I did notice that the Ping))) sensor could get fooled rather badly when an object disappeared from its field of view.  For example, when pointing the sensor at the ceiling from my benchtop, the distance is reported as a fairly consistent 177±0.5cm.  Waving an object in front of the sensor got reasonable readings, but removing the object caused the sensor to get stuck reporting 50.5±1cm, though there was nothing at that distance.  Sometimes the sensor returned to the 177cm reading, sometimes to the 50cm reading, and I’ve not been able to figure out what causes the difference.  The MaxBotix sensor has different dropout problems, sometimes missing the echo and reporting a very long distance, but generally seems to be a little more stable.

What to do before next week’s lab

1. Plot the sensor readings vs. the actual distance.
2. Do linear regression to get a predictor of actual distance given sensor reading.  (Caveat: need to plot distance vs. readings rather than readings vs. distance to get best fit for calibration.)  What is the relationship between the speed of sound and the slope of the line?
3. What is the accuracy and precision of the measurements?  What range of distances can be measured? Is the accuracy better expressed in terms of absolute error (±5mm, for example) or relative error (±1%, for example)?
4. Fix the Arduino program to get better estimates of the distances from the sensors, if possible.
5. Get a recording program working to record a series of measurements of a moving object.

What to do in next week’s lab

1. Redo the Maxbotix calibration the same way we redid the Ping))) calibration, collecting min and max time of flight and using better distance measurements.
2.  Use either the Ping))) or the Maxbotix sensor to record the movement of a simple object away from the sensor and plot the motion.
3. Write a Vpython program that simulates the motion, using only a few constants, not a table of positions or velocities (that is, approximate the motion as constant velocity or constant acceleration).  The simple object could be a small vehicle made from Lego (motorized or not), a mousetrap car, a rolling ball, a falling ball, or whatever else is easy to measure.

Other homework

• Read Chapter 2.
• Work problems 2P38, 2P40, 2P62, 2P63, 2P66, and 2P69.
• Do computational problem 2P72.

We had the first official meeting of the home-school physics class today.  It was just my son and me. Originally we were going to have a second student, but he was busy with college application essays, and asked if he could start next week instead.  My son compared his and my solutions to problems 1P89, 1P97, 1P98, and 1P117 (all the non-computational problems from Chapter 1 of Matter and Interactions).  We got all the same results, but I had left out the units on one of the intermediate steps on one problem—a bad habit that I will try to break, as I agree with John Burk that one should tell the full story of the number, throughout a computation.

In Physics Lab 1, I outlined the first experiment for my home-school physics students and me to do, using an ultrasonic rangefinder.

Here is what I proposed:

1. Hook up the rangefinder to the Arduino and program the Arduino to keep taking measurements and reporting them to the serial line.
2. Calibrate the sensor by placing it at carefully measured distances from a hard wall and recording the readings.  Repeat at several different distances.  (Record temperature, humidity, and barometric pressure, if possible.)
3. Plot the sensor readings vs. the actual distance.
4. Do linear regression to get predictor of actual distance given sensor reading.  (Caveat: need to plot distance vs. readings rather than readings vs. distance to get best fit for calibration.)
5. Modify Arduino code to use the calibration parameters to provide better distance measurements.
6. Re-calibrate using new code.  What is the accuracy and precision of the measurements?  What range of distances can be measured? Is the accuracy better expressed in terms of absolute error (±1cm, for example) or relative error (±5%, for example)?
7. Open-ended: Experiment with detecting different targets (maybe flat targets from wall size down to the size of a quarter, maybe targets of different materials, maybe spherical targets).  What effect does target size, shape, material,  … have on range and accuracy of the measurement?

What we actually did:

My son and I each picked one of the rangefinders (I bought a Maxbotix LV-MaxSonar-EZ2 and a Ping))) sensor), and separately wrote Arduino code to read them. He chose to use the Maxbotix in the pulse-width mode, which is uncalibrated, but which has the greatest resolution.  I used the Ping))) sensor, which has a similar pulse-width mode.  The biggest difference is that the Ping))) needs to be triggered, while the Maxbotix repeats the measurement several times a second.  He had to solder a header onto the Maxbotix in order to connect it up, while I could cheat a little and plug the Ping directly into the Arduino board.  We could probably arrange to have both sensors on the Arduino at once, but have not tried that.

Both of us failed to get busy-wait loops with digitalRead() to work, but we both managed to get pulseIn() to work.  He just reported time in microseconds (then he had to go off to his improv class).  I spent a little more time adding a computed speed of sound (with temperature correction, but not humidity correction), to report distances in cm.  The repeatability of the Ping))) seems pretty good: about ±1mm, but I’ve not tried to calibrate the accuracy yet.  I don’t know whether the limit on the resolution is the coarseness of the pulseIn() measurement of time or variation in the pulse width output by the sensor.

For next week:

My son still needs to do more work on the prelab writeup about how an ultrasonic rangefinder works, so I hope that both students will have drafts of that for next week.  Also assigned for next week is a Vpython programming assignment (Exercise 1p123).

In lab next week we’ll compare our programs for 1p123, then do some calibration experiments with the rangefinder, or try using it to record a series of time and distance measurements for a moving object, or try learning to use Tracker to do video analysis.

I asked physics teacher John Burk for advice on putting together labs for homeschooling my son in calculus-based physics using the Matter and Interactions book (see School decisions part 3 on the decision to homeschool).  He was kind enough to pass on my request to the readers of his Quantum Progress blog: The ideal lab experience for a homeschooled student.  He also gave me a suggestion for a piece of lab equipment we could use for a number of experiments in Newtonian mechanics: an ultrasonic rangefinder.

This post is my first attempt at a physics lab assignment for my son. (Note: we are also hoping to use tech writing this year to satisfy some of his English requirements, so the assignment is a bit heavier on the writing than might otherwise be appropriate for a physics class.)  The exploration in this lab is more engineering than physics, but familiarity with measuring tools is a good place to start, I think.

I welcome feedback and suggestions, particularly from those who have taught physics!

Lab 1: ultrasonic range finder

Prelab

Research how an ultrasonic range finder works (note: as of 25 Aug 2011, the Wikipedia article is a terrible stub—other sources will be needed).

Write: Write a paragraph or two explaining how an ultrasonic rangefinder works.  This should be at a reading level and level of detail suitable for replacing the current Wikipedia stub. Explain what determines the precision, accuracy, and range of the range finder.  How frequently can it measure the range? How is the speed of sound involved?  What does that depend on … ? Why do some have one transducer and others have two?  Audience: new robotics club members (technically interested high school students without prior knowledge of physics or electronics).

Bonus audience: if the writeup is good, it can replace the current Wikipedia stub.

Read the product information (and data sheets when possible) for at least 3 different (cheap) range finding modules like the following three four (added one more 1 Sept 2011):

• PING))) ultrasonic range finder(Note: parallax.com also has mounting brackets, servo-mount option for panning, and packages that combine the range finder with other sensors.)
  

  Parallax PING))) sensor

• SRF04
  

  Image of SRF04 from http://www.kronosrobotics.com/an149/srf04_1.jpg

• MaXBotix LV-EZ1, other MaXBotix range finders
  

  MaxBotix rangefinder

• VEX ultrasonic range finder
  

  VEX rangefinder

Choose one of the range finders for us to buy.

Write: justify the choice in writing, doing a comparison of the advantages and disadvantages of each choice.  Give URLs as citations for data used in making the choice.

Sketch out in pseudocode the program needed to read the sensor on the Arduino using a simple busy loop.  What will determine the precision and sampling rate of the measurements?  What will the code do if there is no object in range of the sensor?

Advanced option: sketch out pseudocode for using interrupts instead of a busy loop.

The Lab Proper

1. Hook up the rangefinder to the Arduino and program the Arduino to keep taking measurements and reporting them to the serial line.
2. Calibrate the sensor by placing it at carefully measured distances from a hard wall and recording the readings.  Repeat at several different distances.  (Record temperature, humidity, and barometric pressure, if possible.)
3. Plot the sensor readings vs. the actual distance.
4. Do linear regression to get predictor of actual distance given sensor reading.  (Caveat: need to plot distance vs. readings rather than readings vs. distance to get best fit for calibration.)
5. Modify Arduino code to use the calibration parameters to provide better distance measurements.
6. Re-calibrate using new code.  What is the accuracy and precision of the measurements?  What range of distances can be measured? Is the accuracy better expressed in terms of absolute error (±1cm, for example) or relative error (±5%, for example)?
7. Open-ended: Experiment with detecting different targets (maybe flat targets from wall size down to the size of a quarter, maybe targets of different materials, maybe spherical targets).  What effect does target size, shape, material,  … have on range and accuracy of the measurement?