How a Vacuum Cleaner REALLY Works

Last winter I wrote an article about the suction in a vacuum cleaner. I got started off on the topic because I read something on Wikipedia that didn't make sense to me. They said a typical vacuum cleaner generates a suction of around 20kPa, or six feet of water. That seemed like an enormous amount of suction, and I quickly did a back-of-the-envelope calculation that showed you would only get about one-eighth of that.

It turned out to be one of my most-read blogposts, and generated a far bit of feedback, much of it supporting my calculation. And yet there were still people telling me that the manufacturers did indeed claim specs of 20-odd kPa, and I couldn't explain it. Maybe those were central-vac systems using multi-stage blowers? I just didn't know.

Last week my wife and I were passing by a little vacuum repair shop at Sargent and Arlington, and she remembered that we needed a filter for our old Hoover. We went in, and the guy there was about 80 years old. I asked him if he knew how much suction you get from a vacuum cleaner? Eighty inches, he said.

I told him it didn't make sense. Assuming a squirrel-cage induction motor and a single-stage blower, I had calculated the maximum pressure to be a mere fraction of that. "Can you show me the blower assembly?" I asked?

The old man went to the back and quickly returned with a blower. It was a universal-type series wound motor (with brushes)...not the induction motor I was expecting. And he poined at the blower housing...it was a two-stage stack, with the first stage feeding the second to double the suction. It looked quite a lot like this:

You could see it was a DC series motor because the field windings were the same size wire as the armature windings, which only makes sense when the current has to pass through both in series. There is also something called a shunt motor, but that has a completely different speed-torque characteristic, the significance of which I will come back to later. In the meantime, there it was: a high-speed DC series motor.


This changed everything. I had already done the calculation to show that the maximum practical pressure for a single-stage blower was 10 kPa, based on a peripheral rotor speed of 400 fps (beyond which the steel cage is torn apart by centrifugal forces.) The problem was that with an ordinary induction motor you could never get the rpm's to bring you up to those peripheral speeds. But now I was looking at the motor, and it wasn't an induction motor...it was a series DC motor, and right on the nameplate it said 12000 rpm! The whole thing was designed exactly according to the maximum theoretical parameters, giving 10 kPa suction...and the second stage doubled it again, bringing you to 20 kPa. The problem was solved.

But where did I get the idea that the motor was an induction motor in the first place? Shouldn't I have known the difference? Or at least checked my facts?

Well, I have to plead here "guilty with an explanation". It's been a long time since I opened up a vacuum cleaner, and I remember the motor being pretty hard to get at. And I absolutely don't remember ever having to change the brushes. So I was thinking...no, there's no commutator motor.

But that's not the whole reason. There are two kinds of DC motors...series and shunt. You use a shunt motor in applications where you want variable speed, that you can control with a rheostat. If you want high revs, like a router, you use a series motor. That's what you'd almost expect in a vacuum cleaner.

But there is something funny about a series motor which makes it different from all other motors. If you let the motor spin free, without putting any torque on it, it revs up to a tremendous speed. It's because of something called "field weakening", and it's easy to explain. But I'm not going to get into that here, except to show you the typical speed-torque curve of a series motor:

What this graph tells you is that as you follow the curve up towards the left, the speed runs away (the dashed line portion). So how do you test for this on a vacuum cleaner? Easy...you put your hand over the nozzle. I know, I know...it looks like your making the motor work harder because it's fighting againt your hand...but it's just the opposite! The motor works hardest when the airflow is wide open, because now it's doing actual work. When the airflow is blocked off, the motor just spins freely. That's when the speed should run away.

Only it doesn't. Sure, it speeds up a little bit...so will any motor, to a greater or lesser degree depending on the winding design. But certainly not to the extent I would have expected for a typical series motor. So I assumed it was just a common induction motor. Which would limit the speed to 3600 rpm, which would give me a much smaller suction...

So where did I go wrong? How do I explain that it's a high-speed series motor, but you don't see the expected no-load runaway condition?

Answer: Cooling-air bypass! The motor is designed so that even when you cover the suction nozzle, there's still airflow to cool the motor. You can see it clearly on this graph which I downloaded from the Yamomoto Electric Corporation:

The speed curve is labled N, near the top of the graph, and you can see it doesn't change that much from no-load to maximum. But if you look at the legend on the bottom, you can see that the airflow never goes much below 12 liters/sec, to a maximum of 36. That's because of the cooling-air bypass. There's always a significant load on the motor, and that's why the speed doesn't run away. Which fooled me into thinking it was an induction motor.

On my other blogsite, I just ended a post where I quoted Regis Philbin from "Who Wants to Be A Millionaire". On a similar note, I'm going to end this post by quoting Paul Harvey:

"And now you know...the REST of the story."

The Diving Board: A Problem in Structural Theory

When I left off last time, I told you I had gone around asking everybody I could find in Civil Engineering if they could describe the curvature of a diving board. Why do I think this is an important story?

Because no "normal" person would do what I did. I would knock on a professor's door and tell him I needed five minutes of his time to ask an important question. And only one or two told me they were too busy. Or I would go up to students in the lab and tell them I had a special question I wanted them to answer. (And by the way, I didn't target weak students to pad my statistics...on the contrary, I only approached guys I thought were smart.) No one goes around doing that...but I do. And that's why I have a story to tell that no one else has.

But what makes me think MY question was so special? Well, it's like this. I never took structural theory when I was in Electrical Engineering, but there were times when I wanted to do something like estimate the stiffness of an I-beam. And I figured out a way of doing it by assuming that on deflection, it would bend into an arc of a circle...then I could use geometry to figure out the percent deformation, and from Hooke's Law I could calculate the energy change. Then I could go back and equate the (force)x(deflection) to the internal stress energy in the flanges. It was a pretty fair method to get in the ballpark.

Then I got that job working in the Structures Lab, and the first thing I found out was that when you stress a beam, it doesn't necessarily form a circular arc. (DUH!) Why else would we need to glue strain gauges all over the place? And that was Ground Zero for me in Structural Theory.

Then I learned something that amazed me: there is something called the Beam Equation and it is a fourth-order differential equations. I thought Electrical had all the hard math, but we never had to integrate four times. This was something new to me.

I didn't get too far in solving fourth-order equations, but I did notice some special cases which were interesting to me. For one thing, you can indeed bend a bar into a circular arc. That's pretty much what you get if you grasp a bar firmly in both hands and bend it as hard as you can. But in practical structures, that's not the most ordinary situation. A more fundamental case is if you have a bar fixed at one end and you apply a load to the free end. And what I noticed, from doing experiments in the lab, was that the curvature went from zero to 100% as you moved from the free end to the fixed end. And that's the observation I made one day to one of our grad students (who didn't believe me!) that led to the whole business of running around asking people the diving board question.

And for the record, here is how I asked the question. First, I told people that I worked in the lab and we measured everything with strain gauges. Then I said: what do the strain gauges tell us if not the local curvature of the beam? The gauge on top is stretching, the gauge on the bottom is compressing...we read the differential and that tells us how much the beam is curving. I made sure EVERYONE agreed on what we were talking about before proceeding.

Then I drew this picture:

This is the case we want to analyze. Can you sketch a plot showing how the curvature (i.e. the strain gauge readings) varies from one end of the board to another? And then I'd hand them the pencil.

People gave me every possible answer! They'd start at zero and go up...they'd go up in the middle and then come down...they'd curve the graph concave up or concave down...EVERYTHING but the right answer. I think three grad students got it right...one of them was a red-headed girl named Robin (Hutchinson was it?) and I think one of them was an Egyptian named Amr (you really have to trill the "r" to get it right.) But here's the thing...when they got it wrong, I'd tell them the right answer, and they'd say..."no, that's not it" or they'd have some reason like the anisotropic properties of wood that made the simple answer "irrelevant". And a few even said, not without some indignation, that "Engineer's don't need to know anything about curvature!"

How about the professors? I already told you only a minority got it right. There were one or two who were able to reason it out reasonably well, to the point where they were pretty sure that it started at a maximum and decreased towards the right. But most of the ones who didn't know simply didn't care enough one way or the other to even try. I find that shameful. They are professors of civil engineering. Shouldn't they know how a diving board works?

Which brings us to the Structures Group. There were maybe seven profs and I think five got it right. Of these, there were basically two categories...Type A and Type B. Typical of the Type A's was Professor Bruce Pinkney, whose bright shiny dome and beady little eyes (Sorry Bruce, no offense intended but it's so true!) cast a terror.  Pinkney listened to my initial request, and then deadpanned: "I'll give you five minutes". Then he fixed those eyes on me, and while they burned (!) I hurried through my explanation, put the sketch on the board, and extended the chalk to him. He remained seated, raised his right hand above his left shoulder, and made a downward slash to the right. No doubt about it. There was nothing left to say, so I simply left.

What about the Type B's? These included a couple of theoretical profs from India (sorry Ajit, I can't remember their names) who listened to me politely, and then pulled out a scrap of paper, wrote out the fourth-degree differential equations, and then started integrating! Boundary conditions, endpoints...integrate once, integrate again, re-calculate boundary condition, and integrate once more...and there it was: a straight line, slanting down to zero from right to left.

Two very different approaches...and how much they say about the question itself, and how engineering is taught! I was totally onside with Professor Pinkney and the Type A's...my whole way of thinking was that we understand the differential equations by being familiar with certain iconic special cases. For me, that fourth-order equation was meaningless until I saw that the curvature of the diving board was linear going to zero at the end. After seeing that, I could sketch all the integrals and derivatives and see how they all fit into the equation. It made sense!

And what was especially significant to me, and what the University should find troubling, is that those professors (the Type A guys) who acutally knew their stuff...had utterly failed to pass that knowledge on to any of their students!

But what about the Type B professors...those South Asian mathematicians who actually did the integrations on the spot? The horrifying thing is that what they did is what their students are expected to do...on the exams, and by implication, on the job. Now, from a subcontinent of a billion people, you can always find a few hundred with that particular genetic mutation which makes them capable of flawlessly executing that type of abstract mathematics. But what are the chances that a typical Canadian engineering student is going to be able to do that on the job? As a practical way to teach young engineers how to analyze structures, it is a cruel joke. But that's our system. I can tell you that of the three students who got it right, they all did it as Type A's...and of the ninety-seven who got it wrong, not one of them even attempted to do it as a Type B! (Although a couple of the profs who got it wrong did!).

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There is a post-script to the story. Some weeks later, I found out that there was a way to ask the question so that everyone got it right. My problem was that I was talking about diving boards and strain gauges, trying to put it in practical terms so that everyone knew what we were talking about. WRONG. If you want to get the right answer, you have to treat the students like Pavlov's Dogs, and geve them the right stimulus. You have to say these magic words:

"Sketch the bending moment diagram of a simple cantilever beam."
 
And then they all do it flawlessly, without a second thought. 

What's Wrong with Undergraduate Education

I wrote an article last year about what's wrong with high school math. I thought it was a pretty good article. But just last week a guy in Switzerland posted an article about what's wrong with graduate-level education...actually it was his letter of resignation from his PhD studies. It was a devastating critique of the pretensions and self-delusions of higher-level academia, and it instantly attracted a collosal number of hits. It speaks to a lot of the reasons why I never got a PhD.

But in between the high school level and the PhD level, there is the huge field of undergraduate education. I've written a few articles on my other blog about some of my experiences as an Education student, but I have a much more important story to tell about my experience years ago in the Faculty of Engineering. After all, everyone already suspects (at least I would) that Education profs are just a bunch of fad-following pretenders...but engineering? That's got to be for real...isn't it?

In fact, there is a tremendous weakness in engineering education which is a direct consequence of the things that Gene Bunin wrote about in his PhD expose. It's because the whole  of academia...arts, sciences, engineering, what have you...is entirely based on the trickle-down theory of education: that the undergraduates will get an "excellent" education because they are in the presence of high-level academics doing "excellent" research. The theory breaks down because the whole premise of "excellence" in research is based on cliques of professors patting each other on the back for generating meaningless grist for the publication mills.

In engineering the consequence is that instead of studying under practical-minded engineers with real-world experience, students learn from academic Engineering PhD's who wouldn't know the first thing about putting up a strip mall (never mind a bridge, or a foundry!) but know all about how to get "research" published in journals. And a major aspect of this cult of publication is to put supreme value on everything new and "original", which has a flip-side of viewing classical knowledge with scorn and disdain. To most professors, undergraduate education is nothing but a mass of boring formulas that have to be mastered before you are qualified to do "important" research at the "cutting edge of knowledge".

In engineering the harm is double-edged: not only do you have a complete absence of the practical knowledge you are going to need on the job (I never heard of the "Building Code" until years after I graduated!) but the theoretical knowledge...the thing that the education system supposedly prides itself on...is a disaster. Accreditation committees compete with each other to prove that they are maintaining ever-higher standards of "excellence", so the curriculum gets cluttered up with so many advanced mathematical topics that it is utterly impossible for any normal student to understand what he is supposed to be learning. There is no choice but to memorize formulas and drill on problem sets so you can pass the exams. Understanding what you're doing?...that's out of the question.

I never saw the truth of all this more clearly than when I went around the Faculty of Civil Engineering, twenty years ago at the University of Manitoba, asking professors and students the Diving Board Question.

I was working at the time as a Lab Technician in the Structures Lab. My job was instrumentation: we would glue strain gauges up and down a steel or concrete beam, subject it to stresses, and measure the distortion in the gauges. It was quite fascinating, and I found myself learning quite a bit about structural theory. (My undergrad degree was in Electrical. And no, I never saw the Electrical Code either until I graduated.)

Anyhow, one day I had just finished helping  a Master's Student run his load tests, and as I was eyeballing the strain gauge data, I remarked to him that until I had started working in this lab, I had never understood how a diving board works.

"What do you mean?" he asked me. I explained that I never realized that the curvature of the board was everywhere different as you moved down the board from one end to the other...that it didn't simply bend into an arc of a circle.

My friend was still baffled. I drew a sketch to show him what he meant. "That's not how a diving board curves", he said. And he drew his own version, which was different from mine.

This was too much. I had to ask someone else. And the next thing you know, I was going from one grad student to another, setting out the problem and asking for their solution. And everyone had a different answer!

Over the next week I asked maybe fifty grad students and as many undergrads, and seventeen professors. Only eight of the seventeen profs got it right. Of the students, I was appalled to find only three that answered correctly.

This was no trick question, or an accident that could be blamed on one bad undergrad prof. The question I was asking was basically the iconic case of a bending beam...you literally couldn't ask a question more central to the basic understanding of beam theory. And the grad students were mostly international, from the four corners of the world. What I was seeing was a true reflection of the way civil engineering is taught in the universities.

Later I wrote this story up and submitted to the Winnipeg Free Press, where it ran as an opinion piece. I was immediately condemned by the engineering and academic communities. One professor of Electrical Engineering wrote a letter to the paper where he explained that Marty Green was this kind of smart-ass who was known for going around asking trick questions to embarass people. I will never forgive Bob McLeod for that. He was certainly not there when I asked anyone the question, so how would he know? What he did was as bad as the police officers who back each other up when one of them is accused of beating a suspect...it's a lie that people justify by a misguided sense of collegial solidarity.

I can prove that it wasn't a trick question. No, I can't prove it to you or to Bob McLeod, because you weren't there. But I can prove it to myself because I was there. First, I always took great pains to sketch out the situation, discuss what I meant by "curvature", and ask the subject if he understood what I was asking. I even drew little strain gauges on the beam, showing them hooked up to a meter the way I do it in the lab, to show that the "curvature" was exactly the thing that we measured with strain gauges. Only then would I ask him to sketch the distribution of curvature along the board...just as though you had a series of ten strain gauges equally spaced...what would the readouts look like?

I said I would prove it wasn't a trick question...well, that's not the proof. The proof comes later. After they gave me the wrong answer, I would draw the graph showing the right answer, and then I would ask them if they agreed. No, they would shake their heads, that doesn't look right. Or they'd come up with some flim-flam nonsense argument about the anisotropic properties of the wooden board to justify themselves.

That's not what you do when you've been suckered by a trick question. You say, "Oh, of course I knew that. They way you asked the question, it sounded like you asking this." No one said that to me.

There's one more proof that it wasn't a trick question, but I'm going so save that for later, when I take up the question of why everybody gets it wrong. Right now I want to return to the question of why I'm so pissed with Bob McLeod for publically dismissing my case on behalf of the university. I believe that there is a tremendous sickness in higher education and something needs to be done about it. People ask me, well what would you do? I tell them it doesn't matter what I propose...nothing is going to happen as long as people don't recognize that there is a problem in the first place. As long as these profs go running around to conferences, publishing papers and patting each other on the back, and giving each other awards for "excellence", and talking about how they're pushing back the frontiers of knowledge...as long as they don't admit to themselves that something is wrong!...there's no hope. What I did by publishing that article was to open the door a tiny crack, to the possiblity that people should think twice about what goes on in academia.  If Bob McLeod hadn't jumped forward to slam that door shut, I suppose someone else would have probably done it instead. But he's the one who did it, and I can never forgive him for that.



 

Excess Air and The Kenora Paper Mill

My fight with the U of W has been really heating up lately, so I've been distracted from the physics. But something reminded me of a story I'd like to tell, so I thought now is as good a time as any. It's about a paper mill where I used to work in the mid-90's.

I was hired in 1993 as a Mechanical Maintenance Engineer in the Boise Cascade Paper Mill in Kenora, Ontario. I only worked there two years; in that time, the mill changed hands three or four times. It was Abitib-Price, Stone Consolidated, and for all I can remember it might have been Abitibi Consolidated as well. (This despite the fact that it was losing money every single month. For reasons I've never understood, there seems to be more money to be made in buying and selling paper mills than in actually making paper.) The Kenora plant was actually a pulp and paper mill. My responsibilities were mainly on the pulp side. The Maintenance Engineer was supposed to provide engineering backup to the Maintenance Trades (millwrights, welders, pipefitters etc.) and also to identify chronic maintenance issues which could be corrected by redesign or other measures. It was a fantastic job that I went into without really having any qualifications. But that's another story...

Today's story is about the Steam Plant. Steam production is HUGE in the pulp and paper industry, and our boiler plant was fired by natural gas, supplemented by bark and other wood byproducts. If I remember the cost structure of the mill, it was a $500,000,000/year facility with costs fairly evenly divided into five parts: consumables (wood and other material costs), transportation (mainly shipping), energy, wages, and capital depreciation. So Energy was about a hundred million dollars a year, and steam production was maybe thirty percent of that. That's the best I can remember.  (Actually, as I think back on it, it wasn't natural gas at all...it was oil..."Bunker C" they called it. Where did I ever hear of "Bunker C" if not in the Kenora Mill? It was oil, not gas.)

As Pulp Side Maintenance Enginer, the Steam Plant was part of my territory. Since I didn't know anything about boilers, I started hanging around the control room quite a lot, asking questions and generall getting to know the guys. Well, to be truthful, there was just a lot of hanging out going on. But now and then I'd glance at the control screen and ask a question or two. And there was a parameter on the display called "O2", and I asked what it was. "Excess Air", they told me. It was usually sitting around 10%. If it got much higher, they would throttle back the intake vanes on the combustion air blowers.

I did a little research on my own, and learned that to run a boiler efficiently, you needed to use just enough air to completely combust the fuel. It's not hard to see why. Remember that air is 80% nitrogen, which is inert. So the job of combustion is mostly to heat up that nitrogen. Let's say you put in the exact right amount of fuel to consume the oxygen, which is 20% of the air. Then your combustion products (CO2, water vapor, and Nitrogen) will go up the smokestack at whatever temperature....let's say, 1200 degrees. On the way up, they pass through the boiler, where heat is extracted via the heat exchangers. The heat exchangers can only draw down so much heat, because you need a temperature gradient to drive the heat flow. So after leaving the heat exchanger, the best you can hope for is that you've cooled the flue gasses to, let's say, 400 degrees. From a reference point of zero degrees (for the sake of argument), that would be a thermal efficiency of 67%. That would be your theoretical optimum for this process.

But what if you are running with excess air? For the sake of argument, let's say you are putting in twice as much air as you need to combust the oil. Then your combustion products are only going to be 600 degrees, not 1200 going into the heat exchanger. And since they leave the heat exchanger at 400 degrees, you've only extracted 33% of the available energy. You're running your boiler at half the optimum efficiency. And if you're spending 30 million on fuel, that means your sending 15 million dollars up the smokestack.

So where does the 10% excess air figure in on all this? Well, you'd like to run at what the chemists call "stoichiometric conditions"...zero excess air. But there are obviously practical problems with this, which I don't need to get into here. Suffice it to say that 10% excess air is considered a good target for efficient boiler operation. And that's what we were reading on our console.

Except...it said "O2". But that's ok...O2, is air, right? Not exactly. It's oxygen. It took me a while, but eventually I figured out that what we had was an oxygen sensor in the smokestack, and it was reading 10% oxygen. Now, when you bring air into the furnace, it's 20% oxygen. So if you're sending it up the stack at 10% oxygen, you've only burned half the oxygen. You used twice as much air as you needed. And that's what we were doing. We were running at 100% excess air, and sending fifteen million dollars a year up in smoke.

You'd think I would have been a hero for figuring this out, but it didn't work out that way. It's hard to get people to change the way they do things, especially if you're a quirky newcomer who looks more like a mad scientist than a hard-boiled engineer. And to tell the truth, there were some people there who already had a vague notion that the boiler was a bit off, but previous half-hearted attempts to improve it had led to other problems, so it was thought best to let well enough alone. Bottom line, I didn't have the credibility to get the necessary people onside to do what needed to be done.

Fast forward ten years. I was driving home from a trip to Thunder Bay where I had taken part in the local Fringe Festival, performing my Yiddish/English comic operetta "The Ballad of Monisch". And suddenly I was back in Kenora. I thought I'd go visit the paper mill and see if I had any friends left there.

I pulled up near the Wood Plant entrance (the building where they have the debarker and wood chipper), and made my way straight inside where I quickly grabbed an orange safety helmet. (Because a bareheaded visitor would stick out like a sore thumb.) And then I wandered around to some of my old haunts, meeting some former friends and just chilling out. I ended up in the Steam Plant, where the guys were quick to pour me a cup of coffee and enjoy reminiscing about old times. While I was there, I glanced at the console...yes, the "excess air" was still running at 10%.

I thought about it on the way home, and figured out a plan of action. I myself never had the credibility to get this taken care of, but there were some consulting engineers in town who regularly worked out at the mill, and if they approached management with the idea, surely it would be taken seriously. On Monday morning, I phoned Dave MacMillan, senior parter at KGS Engineering, and told him I had figured out a way we could make about half a million dollars each in commisions by fixing the steam plant in the Kenora Mill.

"Marty, have you read the papers this morning", Dave asked.

"No, what difference does that make?" I answered.

"I think you should read the papers, Marty." Okay. I went downstairs and looked at the front page. "Kenora Mill to Shut Down". It was over. No one was going to be making any more money out of Boise Cascade, or Stone Consolidated, or Abitibi whatever they were calling themselves.

The mill was in fact a dinosaur, with oudated equipment and a built-in cost structure that could never compete with the brand-new mills being built in the southern US. But I still wonder sometimes how much longer they might have stayed in business if I'd had the moxy to fight for my ideas back when it might have made a difference.