Gas station without pumps

2017 February 5

Units matter

Filed under: Circuits course — gasstationwithoutpumps @ 11:37
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I was a little surprised by how many students had trouble with the following homework question, which was intended to be an easy point for them:

Estimate C2(touching) − C2(not touching), the capacitance of a finger touch on the packing-tape and foil sensor, by estimating the area of your finger that comes in contact with the tape, and assume that the tape is 2mil tape (0.002” thick) made of polypropylene (look up the dielectric constant of polypropylene on line). Warning: an inch is not a meter, and the area of your finger tip touching a plate is not a square meter—watch your units in your calculations!

Remember that capacitance can be computed with the formula C = \frac{\epsilon_r\epsilon_0 A}{d}~,
where \epsilon_r is the dielectric constant,  \epsilon_0=8.854187817E-12 F/m is the permittivity of free space, A is the area, and d is the distance between the plates.

The problem is part of their preparation for making a capacitance touch sensor in lab—estimating about how much capacitance they are trying to sense.

There is a fairly wide range of different correct answers to this question, depending on how large an area is estimated for a finger touch. I considered any area from 0.5 (cm)2 to 4 (cm)2 reasonable, and might have accepted numbers outside that range with written justification from the students.  Some students have no notion of area, apparently, trying to use something like the length of their finger times the thickness of the tape for A.

People did not have trouble looking up the relative dielectric constant of polypropylene (about 2.2)—it might have helped that I mentioned that plastics were generally around 2.2 when we discussed capacitors a week or so ago.

What people had trouble with was the arithmetic with units, a subject that is supposed to have been covered repeatedly since pre-algebra in 7th grade. Students wanted to give me area in meters or cm (not square meters), or thought that inches, cm, and m could all be mixed in the same formula without any conversions.  Many students didn’t bother writing down the units in their formula, and just used raw numbers—this was a good way to forget to do the conversions into consistent units.  This despite the warning in the question to watch out for units!

A lot of students thought that 1 (cm)2 was 0.01 m2, rather than 1E-4 m2. Others made conversion errors from inches to meters (getting the thickness of the tape wrong by factors of 10 to 1000).

A number of students either left units entirely off their answer (no credit) or had the units way off (some students reported capacitances in the farad range, rather than a few tens of picofarads).

A couple of students forgot what the floating-point notation 8.854187817E-12 meant, even though we had covered that earlier in the quarter, and they could easily have looked up the constant on the web to figure out the meaning if they forgot.  I wish high-school teachers would cover this standard way of writing numbers, as most engineering and science faculty assume students already know how to read floating-point notation.

Many students left their answers in “scientific” notation (numbers like 3.3 10-11 F) instead of using more readable engineering notation (33pF). I didn’t take off anything for that, if the answer was correct, but I think that many students need a lot more practice with metric prefixes, so that they get in the habit of using them.

On the plus side, it seems that about a third of the class did get this question right, so there is some hope that students helping each other will spread the understanding to more students.  (Unfortunately, the collaborations that are naturally forming seem to be good students together and clueless students together, which doesn’t help the bottom half of the class much.)

2016 October 5

Broken bike seat

Filed under: Uncategorized — gasstationwithoutpumps @ 17:25
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Yesterday was not a good day for me.

First, I spent most of the day struggling with the homework for the control-theory class I’m sitting in on. The course is dual listed as an undergrad and grad course, with shared lectures but different homework and projects. The undergrad part of the homework was straight-forward, and I finished it Monday night, but the two additional problems for the grad students were tough.  One of them had a simple “engineering” solution that I got quickly by formal manipulation of the formulæ, but I could not justify some of the steps, since they involved a integral that was not finite.  The other problem was not difficult, but involved a rather tedious amount of algebra to linearize the system—the professor had done the linearization in lecture notes,  and we were just supposed to check it for the homework, but he’d made an error in algebra, so I had to redo the whole thing.

Late in the afternoon, I decided to take a break and replace the sump pump that had failed sometime in the past couple of weeks.  Originally I was going to disassemble the pump and see if the problem was repairable (I think that the switch for the float is not turning on reliably, possibly from corroded contacts), but I decided that I could do that later to have a spare pump, meanwhile getting a working sump pump.  (My house is built over a seep where an aquifer comes to the surface, and the water table is about 3 inches below the surface—during wet years, the water table is sometimes right at the surface.)

I put the old pump in my panniers and headed down to hardware store, when my bike seat suddenly failed.  I tried riding for a block with the failed seat and gave up and returned home.  The failure was right at edge of the block that holds the horizontal crossbar at the front of the seat:

Here is a view from the front showing the tubing displaced vertically from where it belongs.

Here is a view from the front showing the tubing displaced vertically from where it belongs.

A closer view shows a very clean break right at the surface of the block that clamps around the tube.

A closer view shows a very clean break right at the surface of the block that clamps around the tube.

I probably should have had some warning about the imminent failure, as the bike has been creaking a bit more than usual when I pedal for the past several months, but I was never able to track down the creaking. I’m not sure I could have seen the crack that was probably propagating, since it was flush with clamp block.

The seat on my Longbikes Vanguard is not a standard, off-the-shelf component, so I’m probably going to have to custom order a new seat from the manufacturer (who no longer make the Vanguard model, so probably has no spare seats built) and wait weeks or months for one to be built.

I got my old upright bike down from the garage wall, inflated the tires, adjusted one of my panniers to fit the different rack, and headed off to the hardware store, carrying the old pump in the pannier. At the hardware store, I could not find a sump pump with the same outlet size as the old one (they all had bigger outlets). I needed to match, in order to hook the sump pump up to the existing plumbing. Luckily, they did have a reducer that would adjust for the difference.

After buying the pump, I went out to my bike and realized that I couldn’t fit both pumps into one pannier—in fact the new boxed sump pump wouldn’t fit into the pannier even by itself. Normally I carry a bungee cord or two for strapping stuff onto my rear rack, but those were left on the other bike. So I had to go back into the hardware store to buy some new bungee cords—not a big deal, but an irritation.

The bike was a bit wobbly on the way home—I’d forgotten how much difference a high center of gravity makes on an upright bike—and the bike has much twitchier steering than my recumbent anyway—but I got home without incident.

On getting home, I immediately attached the pluming to the new sump pump and lowered it into the sump. Let me correct that—I tried to lower it into the sump, but it wouldn’t fit. The pump was a couple of inches wider than the old pump and though the hole at the top was more than wide enough, it narrowed significantly where the bottom of the foundation for the house spread out, and the remaining hole was simply too small for the new pump. This was particularly frustrating for me, as I was meeting my wife downtown for dinner in less than an hour, and I was going to have to walk rather than bike, so I only had about 10 minutes to come up with a fix.

I then remembered something that should have occurred to me much earlier—I had another one of the small sump pumps in a different sump in the back garden. Quickly pulling it out and attaching the plumbing got the main sump working again (though I still need to recheck the plumbing for leaks). And it turned out that the garden sump was wide enough to accept the new pump—problem solved!

I cleaned up, grabbed a backpack so I could do some shopping after dinner, and walked down to the library to meet my wife. After the stresses of the day, I felt the need for comfort food, so we went to Betty’s Noodles, a hole-in-the-wall Chinese restaurant in the bus station. This restaurant has taken over the niche that Little Shanghai used to fill of providing cheap, tasty Chinese fast food (noodles and rice bowls).  I had ma-po tofu over Chow Fun noodles, which went a long way to de-stress me.  Going to Mission Hill Creamery for a plum sorbet cone afterwards helped also.

On the walk home, a couple blocks before we got home, I realized that I had not done my shopping! I decided not to go back downtown, but to do without my chocolate soymilk for a couple of days, until I can go shopping again.

This morning I finished the homework and submitted it. I’m still a bit bothered about the inverse Laplace transform problem that  can be formally solved but that ends up with a function that doesn’t have a Laplace transform, but I’m pretty sure I did what was expected. After turning in the homework, I realized that there was a possible different interpretation of part of the linearization question than what I did, so I queried the professor about what he really meant.  (The homework isn’t due for a week, so if there is a clarification needed, he can get it to the grad students before the homework is due.)

The TA does not grade my homework, since I’m just auditing, but I’m doing the homework using Python instead of Matlab, so I’m sharing it with the TA and professor anyway, so they can see whether it would be worth switching to free tools.

Currently, the scipy.signal package and matplotlib seem as easy to use at Matlab, but there is no equivalent of SIMULINK, which the professor is relying on for students doing simulations.  I can do the simulations in Python, but setting them up is all text-based, and requires thinking explicitly about the state vector, rather than having a GUI that does all the setup for you.

I bicycled up to campus today on my old upright, after adjusting my other pannier to fit the rack.  I had forgotten how uncomfortable an upright bike is.  This evening my neck and shoulders are sore, and I have chafing on the inside of my thigh.  I really hope I can get the recumbent seat replaced quickly, so that I can go back to riding comfortably!  It might even be worth taking the seat to a local frame-builder and finding out whether they could replace the tube, even if only for a temporary fix. (Although most of the bike is chrome-moly steel, the seat appears to be all aluminum tubing.)

2015 April 13

Too much prelab homework for microphone lab

Filed under: Circuits course — gasstationwithoutpumps @ 22:54
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In putting together the book for this quarter, I added exercises to some of the chapters, and I assigned a chunk of them due today as the pre-lab exercise for the microphone lab.  I just spent over 3 hours grading the set, just marking questions right or wrong. There were too many questions, and even the best in the class got only 8/11, with the bottom of the class getting 3/11. I think that the class is doing better this year than previous years’ classes, but some of them got discouraged by how much and how difficult the homework was.  The amount was certainly more than I had intended, but next week’s homework should be substantially less.  I’ll have to figure out how to distribute the load more evenly next year.

I spent most of today’s lecture going over two of the questions (in response to student request), and I’ll have to do some of the other ones on Wednesday, in addition to showing them how to model DC behavior of the FET in the electret microphone. I may also ask the group tutor for the class to have an extra help session this week.  The two questions that got asked about were the modeling of the oscilloscope probe and computing the sensitivity of the electret microphone circuit with a different load resistor.

Some of the problems students had were ones that can be easily fixed (like that 1/10000 is 0 in gnuplot, because it looks like integer arithmetic—1/10E3 does the right computation, as does 1./10000).  Other problems were fundamental misunderstandings of complex numbers or complex impedance, which may be harder to address.

2014 April 22

Electrodes and load lines

Filed under: Circuits course — gasstationwithoutpumps @ 07:17
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As planned I talked on Monday a little bit about polarizing and non-polarizing electrodes, giving them the the idea that the point of electrodes was to convert between ionic currents in solution and electron currents in wires, and that there was always a redox reaction to do the conversion.  (I did not use the term “redox” though, and I probably should have—I’ll try to work it in casually during lab today.)  I talked about three electrodes:

  • the Ag/AgCl that is used for a lot of bio research, because it is non-polarizing, works well in salt water, is generally non-toxic, and is fairly cheap.
  • stainless steel (particularly 316L), because it is commonly used in implants for its non-corroding, non-toxic properties, though it makes a polarizing electrode, which is not suitable for low-frequency measurement.
  • platinum electrode used for the hydrogen reaction that is the standard non-polarizing reference electrode (and is used in a lot of gel-electrophoresis boxes).

Although I gave the chemical reactions for Ag/AgCl (pointing out that the ion current was chloride ions) and the hydrogen reaction, I did not attempt to do so for stainless steel, because I’m still not sure which of the many oxidation reactions are relevant. I did point out that the steel is kept from rusting mainly by a chromium oxide layer on the surface, and that the same mechanism that prevents rusting also makes stainless steel a poor transducer of electron currents to ion currents.  I’m not sure I got that message across though.

I think that it may be worthwhile, either in lab today or in our data analysis on Wednesday, to mention “redox” reactions by name, and to point out more clearly that the what makes stainless steel good for implants also makes it poor for electrodes—the notion that “metal conducts” may be too strong a prior, as students are not used to thinking about the surface properties of things, but just bulk properties.

For the second half of the lecture, I introduced the notion of load lines, with open-circuit voltage VOC and short-circuit current ISC to figure out the voltage and resistance of the Thévenin equivalent of power source. I then had them work out, as a class, the Thévenin equivalent of a simple voltage divider. They got it, eventually, but I had to work through some stubborn holes in their understanding of simple circuits from physics. I think part of the problem was terminology—they apparently did not know what “short circuit” and “open circuit” meant, which I did not realize was a difficulty until near the end of the time.

I did not get the students any RC impedance or voltage divider questions to work on—I hope we have a little time for that on Wed, before Friday’s quiz. I could assign homework with voltage dividers and RC circuits, but I’m reluctant to assign homework in this class, given the amount of work expected for their lab write-ups. Several students already aren’t doing the homework I do assign—many are not even reading the lab handouts with the pre-lab assignments until just before class, when it is too late to do the work. A lot of lab time has been wasted by students trying to do the prelab work during lab.

2014 January 27

Sixth day of freshman design seminar

Today I went into class with a long list of things to get done, but didn’t quite get to all of them:

  • Feedback on first homework.
  • Look at data sheets together.
  • Get class consensus on resistor values from homework due today.
  • Demo the Arduino Data Logger with the phototransistor and photodiode.
  • Discuss next homework (designing a colorimeter).
  • Start talking about Arduino programming.

The feedback on the homework went pretty much as planned.  I told them that the homework was not graded, but that I had both individual and general feedback on it.  Here is a summary of the general feedback:

  • College homework should be typed.  Professors expect it, even if they never say so.  The one exception is math homework, and I recommend to students that they learn LaTeX and typeset even their math.
  • Homework should always be stapled, not loose sheets, which get separated and lost.
  • Hand-drawn pictures are ok for this class (and many other classes), but I strongly recommend learning to use a drawing tool.  Adobe Illustrator is a popular one for those who have money, but Inkscape is an adequate tool for 2D diagrams and is free, though its user interface is rather clunky.  For more professional engineering drawings, I believe that AutoCAD has a free (or very low-cost) version for students. Sketchup and Blender are popular free tools for 3D modeling.  For schematic capture, I now use DigiKey’s SchemeIt, which I demoed briefly for the students (after having some trouble with the wireless connection in the room—I’ll have to check to see whether there is a live DHCP port by the projector cable in the room).
  • Most students added little to what we did in class. I pointed out that K–12 teachers mainly wanted them to spit back what they had been told, but that college professors were usually looking for added value—stuff from reading outside class or from original design.
  • I pointed out the importance of vocabulary (“diffraction” vs. “refraction”, “focus” vs. “collimate”) and of getting the right physical phenomena (Bragg’s Law for diffraction gratings, Snell’s Law and optical dispersion for prisms).  I told them to read the Wikipedia article on optical dispersion, so that they could understand the complexity of determining the wavelength-to-refraction-angle transformation, which is highly dependent on the material the prism is made of.
  • I also suggested that just dumping factoids (like the Bragg’s Law formula) on the paper without explaining the connection to the design didn’t really buy them much.
  • I pointed out the difficult design problem I had given them (300nm–700nm) with a diffraction grating would result in the second diffraction of 350nm at the same location as the first diffraction spot for 700nm—to handle both one would need two optical filters: one for the long wavelength, one for the short.  Even if we limit the range we’re interested in (say to 400nm–700nm), we’d still need a filter, since the sensor would still detect the 2nd-order 350nm spot, even though we weren’t interested in it.
  • I showed a couple of designs for a collimator (a lens and a slit, or a pair of slits on either end of a black tube) and explained why collimation was needed for a spectrometer (none of them had included a collimator).

The feedback took about the amount of time I expected, and I think I managed to communicate the problems without crushing anyone’s egos.  I was careful to tell them that I was not grading them on the homework, but providing feedback for them to do better later on things that would count—particularly that other faculty would often have these expectations of them without ever articulating them.  This freshman class is intended in part to help the students adapt to the college culture in a low-stakes environment.

Simple circuits for measuring light with an Arduino.

Simple circuits for measuring light with an Arduino. Update 2014 Feb 6: Q1 is intended to be an NPN phototransistor, not PNP as shown here!

We then looked at the WP3DP3BT phototransistor data sheet together.  First, I explained the mechanical drawing (dimensions in mm, the diameter sign , the two different ways that the case indicates which lead is which—both the flat and the shorter lead indicating the collector). This prompted a question about the naming of the collector and emitter (since it seemed strange to them that the collector went to the power lead and the emitter to the resistor), so I briefly explained that it was a NPN transistor, that the N’s stood for negative doping resulting in an excess of electrons as charge carriers, and that the emitter emitted the electrons and the collector collected them. I don’t know if that helped anyone.

I then asked the students what they needed help understanding for the numeric part of the data sheet. We ended up talking about 5 of the 7 parameters provided, covering a lot of different things (like that nA stood for nanoamps, not “not available”—a confusion I had not anticipated). I briefly went over milli-, micro-, nano- and explained that engineers preferred using those prefixes to expressing powers of 10, so that the prefer to express the dark current as 100nA, rather than 10-7A. Some scientific calculators provide engineering notation, in which only multiples of 3 are used as the power of 10, and the numbers are between 1 and 999.999999… .

I had to explain the difference between collector-to-emitter and emitter-to-collector voltages, and show the current vs. VCE curve with the two breakdowns. We talked a bit about the saturation voltage (0.8V with an irradiance of 20mW/cm2 and a current of 2mA). I’m not sure I understand that specification that well myself—it mainly tells me that we want to stay well below a 2mA current.

I asked the students for their resistance values from their homework, expecting some fairly random values that would reveal different misunderstandings. What I had not expected is that most of the class had nothing—not even a guess—at the resistance. I would have expected them to ask questions on the class e-mail list if they didn’t understand, but the notion of asking each other (or a faculty member) for help still seems completely foreign to them.

So we spent some time going over how to interpret the on-state collector current: 0.2 nA at an irradiance of 1mW/cm2 of 940nm light. I then had the look for more information that was given in the question, which no one had in front of them:

For Monday, 2014 Jan 27, as individuals (not groups), find a data sheet for the phototransistor WP3DP3BT. Also, select a cheap photodiode that is available in the same size and shape of package as the WP3DP3BT phototransistor and look up its data sheet. For the photodiode and the phototransistor, report the dark current, the voltage drop across the device (that would be collector-emitter saturation voltage for a phototransistor and the open-circuit voltage for a photodiode), and the sensitivity (current at 1mW/cm2 at λ=940nm, which is the wavelength where silicon photodiodes and phototransistors are most sensitive). Find a plot of the spectral sensitivity of a silicon photodiode or phototransistor (it need not be from the data sheets you found—all the silicon photodiodes and phototransistors have similar properties, unless the packaging they are in filters the light). We want to make a circuit so that the full-scale (5v) reading on the Arduino corresponds to an irradiance of 204.8μW/cm2 at 940nm, so that each of the 1024 steps corresponds to an increment of 0.2μW/cm2.

Eventually someone figured out that we wanted a 5v output to correspond to 204.8μW/cm2. I asked what current that irradiance produced. Note that this is a simple linear scaling of the 0.2 nA at an irradiance of 1mW/cm2. It took several minutes for them to do this on their calculators, and several tries before the class agreed on a value (luckily the right one). Now that they had a voltage and a current, I asked them for the resistance that was needed. One student quickly mentioned Ohm’s law, and they set about doing the division. It took them a couple of minutes to do this division on their calculators, and then most of them got it wrong (getting values in the µΩ range!).  Eventually they managed to converge to 122.1kΩ, after almost settling on 12.2kΩ, but what I had expected to be a 30–60-second computation for computing the resistance had taken 10–15 minutes.  The arithmetic and algebra skills of college freshmen are even lower than I had feared.

I showed them a chart of standard resistance values and helped them round to 120kΩ.  I showed them a 120kΩ resistor and measured it with a multimeter to make sure I had the right resistor.  I passed around an Arduino board and a breadboard and explained the point of ther breadboard. I hooked the resistor up in series with the phototransistor (on a pre-prepared breadboard) and used the Arduino data logger to show them the voltage changing as I covered and uncovered the phototransistor. (Next year I should probably reduce the sensitivity they are requested to match to 0.1µW/cm2 per step, as the classroom light was bright enough to move the voltage almost full scale.)

Class had been over officially by 10 minutes at this point (the first time I looked at my watch), so I gave each student a cuvette and asked them to look up what a colorimeter was and design one around the cuvette.

We still need to discuss the photodiode resistance value (I’ll see if anyone figures it out by Wednesday, when I’ve asked them to turn in the homework for real).  We have lab tours on Wednesday, though, so there won’t be time to discuss colorimeters before they design them.  I hope they have the sense to read about them on Wikipedia or the many web sites that give high school labs using them. The actual assignment was

By Mon 2014 Feb 3, design a colorimeter around the cuvette you picked up in class. Your design report should describe the function of the device, explain how it works, have a detailed drawing (with dimensions) of it, have a materials list of what is needed to build it, and give instructions for using it. If there are any computer components, an outline of the needed software should be included also.

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