Quiz Question

One of a continuing series

Airliner crosses Vineland Avenue North Hollywood while landing at Burbank Airport

This is the kind of question that sometimes comes up in engineering.

An engineer is tasked with designing a new airplane, with two requirements. The airplane must be able to carry 8 passengers, and the design must use engine model A3-28, made by the boss’s company.

The engineer completes a design, and then does some calculations. The plane will not fly with a single engine of that model, but it will fly with two engines. The engineer’s boss tells him to modify the design and use two of the engines.

The engineer knows this is a bad idea.


Post your answer in the comments section below.


Hello, I’m the 21st century, and I’m here to take your job.


TRACE, a machine that reads bank checks

I spent nearly 50 years of my life as an engineer, and I think I know when it first started. It was in 1971 that I begin to work in earnest to eliminate people’s jobs.

There was a small engineering consulting company in Austin, and we received a contract from a concern called Autotronic Systems, Inc. Ignoring the name, the company was headquartered in Houston, and they had a chain of self-service gas stations about the country. That was an innovation in 1971, pumping your own gas. It eliminated the job of the smiley attendant, who also checked your oil and wiped your windshield. Our job was to design equipment that fit inside the gas pump and recorded the amount of fuel pumped and the amount charged. The data were transmitted to another device we designed that would store daily sales data and at night phone the home office and transmit the information. Wayne van Citters and I did the software for the home office computer. People lost their jobs.

Two years later  I was working for a company in Irving, Texas, and what they did was build machinery that read the sales receipts from gas stations and did all the sales computation. Their machinery would also read bank checks, printed forms, and mail addresses on envelopes. We eliminated the jobs of the people who previously did this data entry.

In  particular, the company worked on a program to eliminate Post Office workers who eyed addresses and typed them in, or just entered the ZIP code if that was available. Twelve such work stations fed huge machines by Pitney-Bowes that then sorted the mail to the appropriate collection bins. The huge machine was appropriately call a Letter Sorter Machine (LSM). Jobs were eliminated.

I worked a few weeks at a test operation at the Post Office on 8th Avenue in Manhattan, across the street from Madison Square Garden. Postal workers did not like us. There was back room talk of workers sabotaging the machines. Eventually the company I worked for lost the contract to IBM, and I was fired. But the next day I went back  to work for them and did more mischief, eliminating jobs for several more years.

My first patent was for a machine that wrapped a band around a stack of dollar bills. It didn’t have to be one-dollar bills, it would put the strap around 100 bills of any denomination. We sold this system to the Federal Reserve Bank, and my invention eliminated the job of the person who used to put the strap on. Who wanted that job, anyway?

The same company was also a leader in the development of the ATM (automated teller machine). These machines are still around, and they have eliminated thousands of jobs in the banking industry. Docutel was the company that developed ATMs, and it was acquired by Olivetti.

Next I worked on weapons systems for the United States military. You could say I eliminated soldiers’ jobs by automating the work of killing people. My first project involved automating the location of submarines by sonar. I did the software.

My life of developing computer software aimed at eliminating the human element from all manner of tasks. My wife worked for an engineering company, and she was the business manager. She hired me to develop computer software to automate the repetitious accounting tasks. This was before the days of Quick Books.

I finally quit the business of killing jobs four years ago. It’s now the 21st century, and those jobs are not coming back. People are looking for things to do.

Donald Trump campaigned on the basis of a multitude of promises. One promise was to bring back jobs that have been lost in the coal industry. Disinterested parties have looked at this and wondered aloud who would want to go back to working in a coal mine. Nevertheless, idle miners are now looking ahead to going back underground and chewing at the coal seams, or else, sawing off the tops of mountains and scooping up the exposed coal.

But it’s not just safety and environmental concerns that are killing the coal jobs. The 21st century is killing coal jobs. Nuclear power, natural gas-fired power plants, and finally solar and wind power are killing coal jobs. These jobs are not coming back.

Progressive politicians bring us good news. Green power, they promise, will bring back the jobs lost at the coal mines. There is an enormous industry being created to produce wind turbines and solar farms. The new industry will create in the order of 100,000 new jobs, far exceeding the 30,000 lost at the mines.

Not so fast. These green power jobs are not permanent. Once the solar and wind farms are constructed and brought on-line, the industry will only need people to maintain these facilities and to expand them as power needs increase. Unlike coal, wind blows when you are not looking, and the sun comes up every morning. There is no need for the man to shovel sunshine onto a solar panel.

It’s much the same with the automobile industry. Teams of workers who used to assemble automobiles in the United States and in other countries have been replaced by robots. The major industries of electronics and computers would be impossible without the complete automation of just about all processes involved. Watch a video of computer disk drives being manufactured, and you will get an appreciation of the minuscule degree of direct human involvement.

It’s coming to be much the same in all major industries. Retail is eliminating the sales clerk who spends 30 minutes with a customer looking at a $30 pair of shoes without buying. Amazon started it with books, but the trend continues upward. The elimination of human-driven retail drives customer costs down, making it better for the economy all around, but at the cost of out-of-work sales staff.

Will there ever come a time when people will no longer need to be directly involved in producing goods and services? It’s hard to say. Many jobs I (and others) predicted would never go away are now gone for good. Economics, like nature, seeks the steady state. Eliminating jobs reduces the cost of products, but it also eliminates the customer who is supposed to pay for the products. Eventually a balance will be obtained, but at what level? In the meantime, workers are shuffling and trying to adjust, or not. The coal miners of West Virginia just defeated a candidate who promised to eliminate their jobs.

Will workers be able to vote their jobs back? Not likely. When it has been tried it has failed. Communism was a political approach to managing the economy, and it resulted in near 100% employment at the cost of dismal standards of living. This reality killed communism and the Soviet Union, but communism still thrives in the PRC, Vietnam, Laos, and Cuba. I am not mentioning North Korea, which seems to be a special case.

In conclusion, if you recently, or a long time ago, lost your job because of me, don’t bother trying to find me. First, it would not be worth your effort, and second you would be chasing the wrong perpetrator. It was the 21st century that took your job.

Quiz Question

One of a continuing series


There was a previous Quiz Question involving stress concentration in structural members. That got me to thinking about strength of materials. Here is an interesting fact:

First, modulus of elasticity is a measure of the amount of stretch per cross-sectional area for a given load. For example, the modulus of elasticity of structural steel is in the order of 200 GPa. For specially-treated tool steel the modulus is about 207 GPa—not much better. Yet the tool steel will take ten times the load before rupturing. Does this make sense, and why?

Post your responses in the comments section below.

Update and answer

Greg has the right answer. Hardened steel is nor more rigid than structural steel. It just stretches farther before yielding. It’s counter intuitive that something like a hardened tool bit is just as pliable as an untreated steel bar.

Quiz Question

One of a continuing series


The illustration above shows two structural steel rods. The rod on the left is three inches in diameter. It will pull apart at 254,000 pounds. The rod on the left is the same, except the ends are enlarged to five inches diameter. When you pull on the ends of the rod on the right it will pull apart at measurably less than 254,000 pounds.


Post your answer in the comments section below.

Update and answer

Greg provided the correct answer, which is “stress concentration.” In the configuration at the left the stress is uniformly distributed, but on the right the stress is concentrated along the outer edge. Some background.

Stress is load concentration, mechanically equivalent to pressure. It is, for example, pounds per square inch. Strain is an objects response to stress. Strain is deformation induced by stress. Strain is a dimensionless quantity, such as inches per inch. It is deformation in inches per total length in inches.

It is not stress that results in failure of a mechanical component, but ultimately strain. For a material, structural steel for example, as you exert a force to pull the sample apart it stretches. The effect is more pronounced in objects made of rubber, and the resulting strain of a steel part may not be apparent. A solid steel bar stretches just like a spring when you pull on the ends, usually not enough for you to notice. Unless you pull really hard. As you pull harder, eventually the steel stops acting like a spring and ceases to offer additional resistance the more you pull. While the load stays constant the steel continues to stretch. The steel has entered into the plastic deformation range.

If you continue to pull you will pull the steel bar apart. This is called rupture, and it’s the failure mode in tension for materials like steel.

When you pull on the sample on the right what you might not notice is that the strain in the center of the bar is not as much as the strain around the outer regions. That is because the extra thickness provided by the shoulder keeps the region adjacent to the narrow section from moving in response to the load. In the shoulder region the center is pulled down farther than the outer region. Within the thin section of the rod the outer region adjacent to the shoulder now stretches more. The strain is greater. The sample on the right, in this example, will start to rupture before the load reaches 254,000 pounds. When the outer region starts to rupture the load shifts to the inner region, and the bar pulls apart before the load reaches 254,000 pounds.

What you see in aircraft structures and in other structures that operate near the limits of materials is great care to reduce stress concentration. To the extent possible, sharp concave corners are eliminated. Structural members that neck down to smaller dimensions do so in a gradual manner.

Quiz Question

One of a continuing series


When you want to turn on the stair lights while going up the stairs, and you want to turn them off once you get to the top, you need this bit of minor technology. The lights are controlled by two switches. One switch is at the bottom of the stairs, and the other switch is at the top. The switches are “double throw” type. That means the switch is connected to two circuits, and the switch has two positions. When you toggle the switch it turns off one circuit and turns on the other. If the light was on, then throwing the switch turns the light off. If the light was off, then throwing the switch turns the light on. Neat.

Now suppose you have a three-story house, and you want to turn the stair lights on when starting up, and you want to turn the lights off when you get to the second floor, and also off when you get to the third floor if you are going that far. How are you going to be able to achieve that? Do you need a new kind of switch?

What if you have a 15-story house?

Post your answer in the comments below.


Some comments have been received, and it’s apparent clarification is needed. This Quiz Question involves single-pole, double-throw switches. Here is how a SPDT switch works:


Update and Solution

The two-switch feature can be extended to more than two switches, but the configuration I had in mind does not work. I had to go to Wikipedia for a workable solution. First, here is how the two-switch configuration works.




Switch 1 and Switch 2 are SPDT switches. In the first configuration no power is supplied to the load, which is typically a lamp. In the second configuration power is supplied to the lamp, and it turns on.

It is trivial to extrapolate from this and determine that flipping either switch turns on an off-lamp and turns off an on-lamp.

To extend this idea to more than two switch requires a different kind of switch, but still a mechanical switch. The following are from Wikipedia:

Readers are invited to visit the Wikipedia article, following which they will be able to install multi-way lighting switches for their five-story condo.

Quiz Question

One of a continuing series


Steve and Greg, hold off answering this week’s Quiz Question until some others have had a crack at it.

When you go into Home Depot and purchase some electrical wire, you will notice it comes in different sizes. Wire diameter is specified by its gauge. The deal is the smaller the gauge the thicker the wire. You may not also know that a similar gauge system is used for sheet metal. 8 gauge sheet is getting toward boiler plate thickness. 32 gauge is some thin stuff.

When it comes to shotguns, a gauge system is used to specify the bore. The very common 410 shotgun is not a gauge measure. I could be wrong, but I think a 410 has a 0.410-inch bore. The only common shotgun gauges I know are 10-gauge and 12-gauge. Doesn’t matter.

This week’s Quiz Question is, how is a shotgun gauge determined?

Provide your answer in the comments section below. No need to post your answer on Facebook. I always do that when I post the answers.

Quiz Question

One of a continuing series


Here’s something that came up a few years ago. It has to do with GPS technology, but you don’t need to be GPS-savvy to appreciate it. It goes like this.

GPS employs 32 satellites, whose position is at all times precisely known. Each satellite broadcasts to Earth continuously. The signal contains a lot of stuff, but the critical information from each satellite is:

  • I am here.
  • The time is …

A GPS navigation receiver doesn’t need to know the direction the signal is coming from. All that is necessary to determine your position is the preceding information from each of three or four (four is best) satellites.

From the information received, a navigator can determine where all satellites were at the same time. And it can determine how long it took each satellite’s signal to reach the receiver. Knowing the speed of propagation of the radio signal, the receiver can compute the distance to each of three (or four) known points in space and therefore compute its own position in 3-D space. If it knows the speed of propagation of the radio signal.

The problem is the speed of propagation through the atmosphere to the receiver is not constant. It varies due to the presence of free electrons in the atmosphere. There are two solutions to this difficulty. One is to incorporate an atmospheric model into the receiver’s computation, and this is done. It’s called the Klobuchar model, after the person who developed the mode. It’s not very accurate.

For extreme accuracy, the atmospheric delay can be measured directly. To do this, a second transmission channel is incorporated.

The two satellite transmission channels are called L1 and L2. All receivers can use L1. L2 is encrypted. You have to have a secret key, available only to the U.S. government, to use the L2 channel. The two channels operate on somewhat different frequencies, and the atmosphere delays each channel differently.

And that’s all you need to know if you can receive both L1 and L2. You do not need to know in advance how the atmosphere delays each channel. The receiver can deduce the atmospheric delay from each satellite, and from that it can compute the position of the receiver to very high degree of accuracy.

When I first encountered this it was obvious to me there was not enough information to compute the atmospheric delay. So I asked a guy working on the project how this was supposed to work, and he stopped what he was doing and explained it to me. I still didn’t understand it, but I took my notes back to my cube and looked at it some more. It was an “oh shit” moment. “Of course, dummy.”

And that’s this week’s quiz question. How can a GPS receiver compute the atmospheric delay from the information given, using L1 and L2?

Post your answer as a comment below. I’m going to give this a few days and then post a hint.

Update and hint

I’ve had no activity on this Quiz Question all week. It’s time to provide a hint. Look at the problem again.

You have two radio signals originating from the same location at the same time and arriving at the receiver at different times. Because of ionospheric delay, you don’t know how long it took either signal to traverse the unknown distance to the transmitter. How can you use the information available to determine the distance to the transmitter. Here is the hint.

The satellite is moving. In the order of miles per second. Its distance from the receiver changes from one transmission to the next. How can you use multiple measurements to compensate for the ionospheric delay?

Update and solution

Time’s up. I need to post the solution to last week’s Quiz Question, because tomorrow’s question is going to be related to compensating for ionospheric delay. I’m not going to do the math. Instead, I’m going to pose the question in a different way that will make the solution obvious. It goes like this:

Forget satellites. There are two rail lines running parallel for miles over the horizon. You’re standing at a point along the rail lines waiting for two trains (call them A and B) to arrive. The two trains are going to start at the same time from the same location, and they are going to come at you at different speeds. You don’t know what the speeds are, but you know the speeds of A and B are different, and they are constant.

Trains A and B arrive. A arrives shortly before B. You note the time difference. You don’t have enough information to determine how far away the station (starting point) is. You move down the line a few miles, carefully noting how far you move.

Two more trains, also labeled A and B head your way from the station. Same as before. A arrives, then B arrives later. You record the time difference. Of course the difference is greater, because you are farther from the station, so the trains have had longer to diverge.

Now you ask yourself this question. “How far do I have to walk toward the direction the trains came from for the difference to be zero?” That’s the distance to the station.

In the case of GPS with channels L1 and L2 it’s the satellite that moves, and since the satellite is always telling you where it is, you know how much farther (or closer) it has moved from you between two measurements.

There is obviously more to it, so if anybody still has questions, post a comment and extend the dialogue.

The Math Solution

I watched this the first couple of seasons when it came out in 2005, before I became averse to TV drama shows. I’m reviewing this episode because of something in the plot that piqued my interest. It’s NUMB3RS, by Nicolas Falacci and Cheryl Heuton, and it’s about math genius Charlie Eppes (David Krumholtz) and his brother Don (Rob Morrow), who is an FBI agent working in Los Angeles. Charlie, who is a math prof, helps his brother solve crimes by the application of arcane math principles. This is about the second episode of season one.

The plot revolves around tracking a bank robbery gang, and the opening shots show some statistics. Here, 16 banks were robbed, two robbers, average take is $2700, and no weapons employed. These two are called the Charm School Gang, because they are so polite. They even open the door for other customers when entering the bank, and they smile throughout the operation.


Charlie has applied some statistical analyses and has determined an underlying pattern to the sequence of crimes. He has predicted the robbers will strike on a particular day at one of two banks in L.A. The title sequence overlays security video shots from the robberies with math symbols.


The FBI is waiting on the appropriate day, and the robbers strike one of the two banks. Agents rush in to make the arrest, but there is a dramatic turn. Unknown before, the robbers have always had a backup of four well armed henchmen, who never made an appearance before, because they never needed to. In a hail of gunfire an agent is killed, along with one of the bandits. The others make their escape.


The failure of the FBI operation and the death of the agent sends Charlie into a deep funk, and he takes himself off the case, immersing himself at his home in the solution of one of the so-called NP-complete math problems. It’s a class of problems still defying resolution.


The crooks pull off another robbery, this time killing a bank manager. Charlie’s friend on campus, physics professor Larry Fleinhardt (Peter MacNicol) reminds Charlie of Heisenberg’s Uncertainty Principle. It applies to sub atomic particles (and even to atomic particles), and it makes us aware that measurement, observation, of an entity requires some interaction with it, thus affecting the thing being observed. This is critically true of sub atomic particles, but Charlie is reminded that macro objects, such as bank robbers, are also affected when they are observed, particularly when they are made aware they have been observed, such as the FBI presence at the previous robbery.

And Charlie has more. This is a world-class operation, armed to the hilt, military coordination, with six skilled operators involved. For an average of $2700 a whack? Something is wrong. Charlie figures out with it is. They are not robbing banks. They are using the robberies as a cover for another crime. The crooks are stealing bank transaction data. While everybody else is preoccupied with the heist, somebody is slipping over to one of their computer terminals.

The robbers are after bigger stakes. They are tracking the schedule for the delivery for destruction of millions of dollars in unfit currency by the Federal Reserve Bank. They are going to hold up the cash transfer.

Don and the FBI team prepare to intercept the heist. Charlie is there. He reminds Don of the Heisenberg Uncertainty. The gang is likely aware the feds are on to the scheme. Don tells Charlie to not worry. They are well prepared for the Heisenberg Principle.


Sure enough. The bandits intercept the shipment. Sure enough, they get the drop on the FBI agents.


But Don and the other agents are one step ahead. They know the bandits know, and they have anticipated the getaway plan, killing one of the bandits and capturing the others. Here Don says hello to the ring leader as he attempts, unsuccessfully, to start the getaway car.


And here is my Skeptical Analysis—it’s something I picked up on in my working life. Since I never had a real career, just a succession of jobs, I ended up working with a wide range of technologies. My first patent involved the Federal Reserve Bank. They wanted a machine that would automatically put a strap around a bundle of 100 bills. In the course of this project, I visited the Federal Reserve Bank in Dallas and got a look at their operation. And I saw what they do with unfit currency. They do not, as the TV plot would have it, take bundles of currency to a secret location for destruction. They destroy it right on the spot.

In the basement of the Dallas branch were hand carts loaded with tremendous stacks of currency. Particularly, there were some carts loaded with unfit currency. You could tell. Each bundle of 100 had been drilled through, leaving two 1/2-inch diameter holes in each bill. These bills were worthless. Further destruction of the bills was rendered by a hammer mill, and the chaff was sold off for planters mulch and such.

The project I worked on went a step further. It eliminated the need to drill the two holes. My company sold the Federal Reserve a system that accepted stacks of bills into a feed hopper and peeled them off at high speed, feeding them into a document transport. As each bill passed down the length of the machine various readers detected counterfeit, which was routed to a special bin. Other stations recorded denomination, serial number, and such. Another station detected unfit currency. Unfit currency went all the way to the end of the machine, about ten feet, and entered a high-speed shredder.

And that’s what I found screwy about this plot. The writers could have patched this up a bit and made it true to life. But then, this is fiction, and it’s OK to give the imagination free rein.

Quiz Question

One of a continuing series


There once was in Carrollton, Texas, at the intersection of Belt Line Road and Webb Chapel Road a concern called Otis Engineering. I was by there for a visit. They made “down-line” equipment for oil wells. This was stuff that went down into oil wells, sometimes miles deep, to make measurements and such.

They had a pressure chamber for testing their stuff, and this chamber was well-armored, to withstand those deep pressures. They filled it with water and applied the pressure. They took great care that there was no air in the chamber. Why was that. What would be the problem if there were some air in the pressure chamber?

This one is some basic science and I expect some quick answers. Provide your response in the comments section below.

Update and answer

Greg has answered this one, but I do not see evidence he has posted a comment. The reason is this:

A body of water under pressure represents an amount of stored energy to the extent it is compressed. Air is multiply-compressible over water, and at great pressures can story a dangerous amount of energy. The potential energy of a compressed fluid is proportional to the pressure and the square of the compressed volume. Since water compresses very little under great pressure, compressed water does not represent so much potential energy. Any gas in the chamber, however, would be compressed tremendously and would represent a large amount of potential energy.

Greg is correct in that it would take more energy to raise the pressure of the chamber if had some air in it. However, the real concern is the danger of releasing the potential energy accidentally.

Adventures In Hyperspace

Examine the following:


That’s pretty dull. It is something familiar to any school child, even those not majoring in math or science. The horizontal line is the x-axis of a coordinate system, and the vertical line is the y-axis. They are said to be orthogonal. They are orthogonal in two senses of the word: they form a right angle, and they are mathematically orthogonal. In the second sense measurements along the x-axis are independent of measurements along the y-axis. You can move all you want in the x-direction without affecting your position in the y-direction.

There’s more. For example, suppose x and y represent east and north. Then up can be represented by z. Now we have a system of three coordinates, and they are mutually orthogonal. Movement in the up direction does not affect your position in the east and north directions.

You may need to close your eyes to imagine the next part, but you can add a fourth orthogonal coordinate to this representation of space, and you will have a four-dimensional space. I can’t draw it, so I have to deal with it in a purely mathematical manner. The principles of geometry that hold for three-dimensional space can be extended to higher-dimensional spaces. And that’s what I did.

Next look at this image.


The curve comes down from the left, reaches a low point and then continues upward to the right. The task is to locate the low point of the curve. You want to do it by an automated process for reasons that will be made clear later. The straight line is tangent to the curve as shown, and the short vertical line is the x-coordinate at the point of tangency. If you have a mathematical function for the line you can compute the derivative of the function, and the derivative is the slope of the tangent line. You can see that the slope of the tangent line will be zero at the low point, so if you find the point at which the slope is zero, then you have determined, mathematically, the x-coordinate of the low point—the minimum value of the function.

See the diagram.


The problem of finding the minimum point of a function devolves into finding the point at which another function, the derivative, is zero. There is a mechanical process for finding the zero of a function, and it’s called the Newton-Raphson method, after Isaac Newton and Joseph Raphson. The utility of this method is it can be performed by a computer.

Now suppose that what you have is not a line function but a surface function. My Microsoft Excel was not able to draw such a surface, so I obtained this one from Wikipedia.


You can find the low point (minimum) of this surface by a method similar to the one above. And that’s what I had to do. There was a project I worked on, no government secrets involved, and we were flying a Convair transport plane carrying multiple imaging systems. We collected visible, infra-red, and laser radar images, and when we got them all back to the lab we needed to determine what the system was looking at at for each image. To do this we needed to know where the airplane was at the time the images were made. As accurately as possible.

We had multiple sources of information. We had an inertial guidance system (INS) and a transponder locater system. And we had more. The problem was the sources of information were in disagreement about where the airplane was with respect to time. It was going to be necessary to apply corrections to the various inputs to minimize the error.

Without getting into the details of how I spent three months of my life, I developed an error function based on the data inputs just mentioned, and my goal was to apply corrections to the input data in order to minimize the error function. See where this fits in? I needed to compute the minimum of a function.

But this was a function in multiple dimensions. Ultimately it grew to a function in ten dimensions. I needed to minimize a function in ten dimensions.

Inspiration came from the surface function. You can use the Newton method to compute the minimum of a surface if you follow this approach, and if you have a well-behaved function.

Start with one axis, for example the x-axis. Compute the minimum for a given value of the y-axis. That is, move along the x-direction while holding y constant. Compute the minimum of the curve defined by the x-values alone. Once you have done that, switch to computing the minimum along the y-axis, using the x-value for the minimum just computed. Repeat until you have finally reached the minimum of the surface.

What I figured would work was to just continue the process into the higher dimensions. Take each axis in turn, holding the other coordinates constant, and compute the minimum. Then go to the next dimension and the next and the next until you have gone through all the dimensions of the error function. Repeat until the solution does not get any better. You have computed the minimum of a function in multiple dimensions.

There was one small hitch. I did not have math functions for the data, just values from a table. To make this computable I needed to supply math functions, and to get math functions I needed to fit curves to the data points. And that’s another story, which I will delve into in another post.

We ran this problem on a VAX computer, which was no slouch of a system in those days, but which would be in the shade of the laptop computer I’m now using to describe all this. And the VAX chugged through solution after solution and computed the position on the ground the cameras were looking at, and when we pulled up the images associated with well-surveyed points, there were the objects that were supposed to be there. To a certain degree of accuracy. It was never perfect. But that’s the way it is in engineering.

Wait, there’s more. After I did all this I learned of an even better approach. It was in a book I already had on my shelf but had not read from cover to cover. It’s a method by Nelder and Mead, and code is available from the book:

We give in §10.4 a somewhat neglected downhill simplex method due to Nelder and Mead. (This use of the word “simplex” is not to be confused with the simplex method of linear programming This method just crawls downhill in a straightforward fashio that makes almost no special assumptions about your function This can be extremely slow, but it can also, in some cases, be ex­tremely robust. Not to be overlooked is the fact that the code is concise and completely self-contained: a general N-dimensional minimization program in under 100 program lines! This method is most useful when the minimization calculation is only an inci­dental part of your overall problem. The storage requirement is of order N2, and derivative calculations are not required.

[Press, William H., et al: Numerical Recipes in C, Cambridge University Press. 1988 p 292]

Quiz Question

One of a continuing series

One of the last useful things I did during my Navy Reserve tour was work in the Sidewinder shop at NAS Dallas. My first encounter with a Sidewinder was educational. There was one on a work stand, and I looked it over. One thing I noticed was that each of the rear stabilizing fins featured a curious mechanism. See the photos. I have scrounged up three so make sure people can get a good view of what I’m talking about.

On the trailing edge of each rear fin, at the outer corner, is a hinged fixture. The fixture is a flat plate with a solid brass disk enclosed in the plate so that the outer edge of the disk is exposed to the wind stream. The edge of the disk is serrated, and the disk is mounted so it can spin freely on its axis. The air stream spins the brass disk at high speeds. The flat plate is attached to the fin along its leading edge by a hinge so it can freely swing to either side.


An AIM-9 Sidewinder Missile installed on an F-14 Tomcat. The AIM-9 is a short range, heat seeking air-to-air missile.

An AIM-9 Sidewinder Missile installed on an F-14 Tomcat. The AIM-9 is a short range, heat seeking air-to-air missile.


So, when the missile is fired, the brass disk is spinning very rapidly, and it’s mounted in the flat plate, which can swing from side to side. And here is the Quiz Question.

What does this arrangement do? If you are an engineer or a physicist looking at this you will figure it out immediately. Engineers and physicists are invited to have a go at this immediately. Post your answers in the comments section below.


Jim Medding has provided the correct answer that these tabs are used for roll stabilization. He left it for me to provide the mechanism.

This was over 50 years ago, but at the time I first examined this mechanism I was a full time engineering student and a part time Aviation Ordnanceman in the Navy Reserve. About five seconds, and it dawned on me. The tabs work this way:

The outer edge of each brass disk sticks out into the wind, causing the disk to rotate. Applying some basic principles of physics, If the missile rolls (to the right for example), then each disk will be rotated to the right. Because of the direction it’s spinning, the disk will apply torque on the hinged tab and force it to swing to the right, into the air stream on the right side of the fin it’s mounted on. That will produce an aerodynamic force to resist the roll in that direction. Similarly if the missile rolls to the left. These tabs with their rotting disks are an automatic roll stabilization mechanism with a built in control mechanism and requiring no power from the missile control system, which is located way forward on the missile body, anyhow.

It was so slick, I never forgot about it in all this time, and I tip my hat to the engineer who came up with the concept.

Quiz Question

One of a continuing series

See the diagram below. This is how my thermostat works.


When the temperature reaches 76° the cooling comes on. The room starts to cool. See the next.


When the temperature reaches 74° the cooling shuts off. The room will now start to warm up, but the cooling will not come back on again until the temperature reaches 76° again. This feature prevents the cooling system from cycling on and off frequently around narrow changes in temperature. The feature is called hysteresis. The Quiz Question for this week is this:

What does this have to do with women?

Post your answer as a comment below. I will update the post with the answer on Friday.

Quiz Question

One of a continuing series

This one may be too easy. Here it goes anyhow.


In 1962 an Atlas rocket launched from Cape Canaveral went off course and had to be destroyed. The problem was traced to a snippet of FORTRAN code. Here it is:

DO 55 J = 1.100

What’s wrong with this code? What was it supposed to do, and what did it actually do?

People who’ve been programming for more than 50 years are not allowed to answer this question. Give the newcomers a cut at it first. I will update this post with the answer if there is no correct response by Wednesday.


Steve provided the correct answer. With a comma this is the beginning of a DO loop. With a period it becomes an assignment. FORTRAN programmers should know that the FORTRAN compiler throws away all spaces. The space character is meant only for human eyes. Here’s how the above code appears to the FORTRAN compiler:


The compiler responds by creating a new variable named DO55J and assigns it a value of 1.1. No loop is created, and the rocket is lost.

Quiz Question

One of a continuing series

Racers aren’t allowed to answer this one.

The item pictured below is a carburettor jet.

Cycle Pro Pilot Jet for Keihin Carb

Cycle Pro Pilot Jet for Keihin Carb

Before just about everything went to fuel injection, there were carburettors. Carburettors supply a mixture of air and fuel to the intake ports of piston engines. They work this way.

On the intake stroke of an engine, the piston moves down, drawing air into the cylinder. Air flows rapidly into the cylinder, passing first through the carburettor. The air stream through the carburettor, because of its forward motion, exerts reduced pressure against the side walls of the port. The carburettor jet connects the air stream to a supply of fuel in a float bowl, a small reservoir of fuel in the carburettor body. The reduced pressure causes fuel in the float bowl to be forced through the opening in the jet and into the air stream. The fuel mixes as a spray with the air stream and is carried into the combustion chamber.

The carburettor jet has a measured opening for the fuel. A larger opening will allow more fuel to flow into the air stream. Here’s the question. A motorcycle racer (for example) arriving at the track in the morning observes it’s a warm and humid day. He opens up his race kit box and selects a set of jets with larger openings and installs them in all the carburettors in his engine.

Why? Why does the racer know he’s going to need a larger jet?

Provide your answer as a comment below. If nobody provides the correct answer by Friday I will post it here.


The answer to the Quiz Question is that warm air and moist are are less dense. The equation shows the relationship between pressure (p) and density (ρ) for incompressible flow. I’m using this, since no compression or expansion of the air takes place inside the carburettor throat.


The velocity of the airflow is v. The remaining terms are g and z, the acceleration of gravity and the altitude, neither of which figure into the carburettor operation, all other things being equal. For a given velocity, p and ρ must be proportional. If ρ goes down, p must go down. When the air is less dense the pressure must go down. You need a larger opening in the jet to allow the proper amount of fuel into the air stream, else the cylinder will burn too lean. The result would be a burned piston.

Stand by for another Quiz Question on Monday. And keep reading.

Quiz Question

One of a continuing series

An automobile engine, as everybody has experienced, can develop a maximum amount of power at the drive shaft. This is to be expected. The chemical energy available from fuel and air is fixed for a given flow rate, and an automobile engine reaches a maximum flow rate.

How about a rocket engine? Amazingly, rocket engines don’t have this limitation. Here’s an illustration:


Exhaust gases exit the rear of a rocket at a velocity v (lower case v). The thrust accelerates the rocket body in the opposite direction. At any instant it has a forward velocity V (capital V). The thrust produced by the escaping exhaust gases is constant, no matter how fast the rocket is moving.

The power produced by the rocket motor is given by:

W = fV

The power, W, produced by the rocket motor is the thrust, f, multiplied by the forward velocity, V.

How can this be? The rate of chemical energy expended is constant, controlled by the binding energies of the reactant components. These should not be dependent on forward velocity. Yet, as the rocket goes faster more power is produced. Is this a paradox? If so, what’s the resolution of the paradox?

Post your answer in the comments section below. I will provide the resolution by Friday if nobody posts a solution by then.


Time’s up. Nobody has been addressing this week’s Quiz Question recently, so I’m posting the answer.

This Quiz Question is a good illustration of a property of energy, kinetic energy in particular. Kinetic energy is dependent on the frame of reference. Revisit the illustration above. In a particular inertial frame of reference the rocket has zero kinetic energy, even several seconds after firing the propellant charge. At any instant in any particular inertial frame of reference the chemical energy of the fuel is being converted to kinetic energy: kinetic energy of the rocket and kinetic energy of the exhaust. At any instant the energy conversion is divided between the rocket and the exhaust. Here are two examples. The frame of reference is the one in which the rocket has zero velocity at the time the propellant charge is fired:

  • At the moment the propellant charge is fired the rocket is not moving. All the chemical energy from the rocket fuel is feeding into the exhaust gases. The rocket motor is developing zero power.
  • Some time later, the rocket is moving. Some of the energy conversion is going into the rocket, and the remainder is going into the exhaust gases. The total is constant. It is the rate of conversion of chemical energy. The rate at which kinetic energy is added to the rocket is the amount of work done on the rocket. This is the definition of the power of the rocket motor. It is the thrust of the rocket motor multiplied by the velocity of the rocket in the frame of reference defined above.

If  any of these points need additional explanation, paste a comment below.

Next Monday, a new Quiz Question. Some people are going to know the answer immediately.

Quiz Question

Forty-five years ago I worked for an engineering consulting company. We did design and development for companies that did not have their own engineers.

This was at the dawn of self-service gas stations, and new companies were getting into the business. One had a chain of stations called Fill-Em-Fast. It was Autotronics out of Houston. What they wanted was to get sales information on a daily basis. This was before the days of the Internet and instant sales reports. What they wanted us to do was to electronically record sales information, gallons and dollars, from each pump. At night, when phone rates were low, the home office would phone each station in turn and retrieve the sales information from the station’s box. We designed that.

This Quiz Question regards a problem involving the retrieval of sales information from pumps. These were the mechanical pumps of your grandfather’s day. There was a mechanical display operated by gears as the fuel was dispensed. We figured all we needed to do was to hook into the rotation of the gear shafts and read the revolutions, or increments of same. That’s where the following image comes in.


We would fit an extra spur gear on the shaft we wanted to read off and just count the gear teeth as they went by. Don Ninke was the EE in charge of this, and he came up with a design that counted teeth with an optical interrupter. An LED would send out light, and a photo-diode would receive it. Gear teeth would interrupt the beam, and we would count the pulses.

It didn’t work. It counted too many teeth. And that’s the Quiz Question. Why didn’t this work? Why was this design counting too many teeth?

Part two of the Quiz Question: How did Don fix the problem and count the correct number of teeth?

As always, post your answers in the comment box below. I will provide the answer Saturday, or before.


Mike has provided the answer:

Backlash. If you have two sensors, you can tell the direction of motion.
Used this technique on the automobile odometer cable for a time-speed-distance car rally computer.

Mike obviously has had some engineering experience. This is the solution Don Ninke came up with. The applicable term is “quadrature.” Set the two sensors out of phase by 90°. If the gear backs up a tooth, one is subtracted from the count. See the diagram.




Counter rotation of the gear shaft typically occurs when the mechanism stops. There’s not much problem when the pump is running, and the shaft is turning continuously. Discounting spurious pulses has two benefits:

  • You don’t over charge the customer for an extra tooth’s worth of gas.
  • At the end of the day you don’t have have the accumulated error of these extra counts, which would screw up the accounting. There were separate shafts for the dispensed gas and dollars charged. They really need to match at the end of the day.

Interesting thing to note: The only computer used in the system was a Data General Nova 1200 mini-computer. That was installed in the home office in Houston, and Wayne van Citters and I did the software for the Nova.

The electronic box that Don Ninke designed employed no processors. It was all series 7400 logic chips from Texas Instruments. It counted pulses and recorded sales from the pumps, accepted calls over a phone line, and spewed out the sales data for the day over an RS-232 link.

About this time (early 1972) we learned there was a company developing a computer on a chip. We requested and obtained a spec sheet dated late 1971 from Intel. I still have it—two Xeroxed sheets on the 8008 microprocessor. It was an amazing time.

Quiz Question

One of a continuing series

See the diagram below.

For about eight years I worked for a company that made document processing systems. One of the company’s inventions was a high-capacity ink jet printer. It worked as shown.


There was a nozzle that spit out 105,000 ink drops per second. A variable voltage was applied to the nozzle, which charge was retained by each ink drop as it exited the nozzle. The voltage was changed for each drop.

The drops passed between two charged plates. Drops with differing charges were deflected in different directions by an amount proportional to their charge. It was a touchy situation. The voltage needed to be something like 5000 volts between the two plates. Not enough voltage, and the drops would not be deflected enough. Too much voltage, and electricity would arc between the plates. I spent weeks getting a configuration that would work. Ink drops were properly deflected, and there was no arcing.

We installed our systems in major banking and financial centers around the world. Then I asked a question. “Do we have any customers in Denver?”

And the quiz question is this. Why did I ask that question?


Mike apparently saw the answer right away. I asked him to hold off before posting his comment. And here it is.

From high school physics we know that dry air breaks down at 25,000 Volts per inch. That’s dry air at sea level. When the air gets thinner at higher altitudes it breaks down at lower voltages. This arrangement featured two charged plates operating on the verge of breakdown. That was one of the big problems, as noted in the statement of the problem.

It was obvious when we finally got this thing to working that it wouldn’t take much to tip the balance and induce arcing. An increase of one mile in altitude would surely do it.

As it turns out we didn’t have any systems installed in Denver, La Paz or any other troublesome locations.

Provide your responses in the comments below.

Quiz Question

One of a continuing series

Here is a photo from a nearby service station. Note the price of diesel.


The first question is:

1. Why does diesel fuel cost more? That is to say, why are drivers, especially big truckers, willing to pay more?

The second question is for after you answer the first question. It will be revealed after you answer the first question:

2. Why?


There have a few responses, at least one that accounted for some of diesel’s advantage. Prasad commented:

Diesel is denser and longer hydro-carbon chains than gasoline, which is lighter and more volatile. Hence gasoline has less energy per gallon than a gallon of diesel.

Since it can make cars/trucks go farther with the same volume of fuel it is still economical to buy diesel at a higher price than gasoline (for the same volume.)

I guess they are charging it by energy content.

Here are the facts concerning relative energy content:

As of 2010, the density of petroleum diesel is about 0.832 kg/L (6.943 lb/US gal), about 11.6% more than ethanol-free petrol (gasoline), which has a density of about 0.745 kg/L (6.217 lb/US gal). About 86.1% of the fuel mass is carbon, and when burned, it offers a net heating value of 43.1 MJ/kg as opposed to 43.2 MJ/kg for gasoline. However, due to the higher density, diesel offers a higher volumetric energy density at 35.86 MJ/L (128,700 BTU/US gal) vs. 32.18 MJ/L (115,500 BTU/US gal) for gasoline, some 11% higher, which should be considered when comparing the fuel efficiency by volume.

That’s an 11% advantage over gasoline. Since the fuels are priced by volume this gives diesel a slight advantage with the prices shown in the photograph, which shows diesel costing 10% more. In order to get a price advantage that would make it worth while to drive diesel over gasoline, some other considerations need to be taken into account. These would involve the way diesel engines operate compared to gasoline engines.

Gasoline engines throttle the intake air. Diesel engines do not. A diesel engine would not work if you throttled the air intake. Operation of a diesel engine requires a full cylinder of intake air on the compression stroke in order to generate the ignition temperature. Diesel engines don’t use spark plugs. Each cylinder has a glow plug to ignite the fuel when starting the engine. After that the engine relies on injecting fuel into the hot, compressed air in the cylinder.

Diesel engines run at leaner fuel mixtures when the pedal is not pressed all the way down. The throttle is a fuel throttle, not an air throttle. Backing off on the throttle decreases the fuel injected into the cylinder, but not the air.

If you run a gasoline engine lean the combustion temperature goes up, resulting in melted pistons and burned valves. Not so with a diesel engine. Leaning the mixture in the cylinder only decreases the amount of fuel in the combustion and does not raise the combustion temperature.

Also, for comparable reasons, diesel engines typically run at higher compression ratios than gasoline engines. A 12:1 compression ratio is a racing engine for gasoline. Diesel engine compression ratios start at 12:1 and go up from there. Typical would be 14:1. Some engines run at 18:1. Basic principles of thermodynamics produce better fuel economy (more mechanical work from comparable chemical energy) for higher compression ratios.

Diesel vehicles may be making a comeback. Diesel engines are more fuel-efficient and have more low-end torque than similar-sized gasoline engines, and diesel fuel contains roughly 10% to 15% more energy than gasoline. So, diesel vehicles can often go about 20% to 35% farther on a gallon of fuel than their gasoline counterparts. Plus, today’s diesel vehicles are much improved over diesels of the past.

Given this, the 10% hit on fuel price does not look so bad.

Quiz Question

This question never appeared on a quiz. Motorcycle racers are going to get this one fairly quickly. But first the story behind it.

Back in my college days I knew these two racers, Mike Bonnell and John Horn, both college students. They went up to Meadowdale, Illinois, to a professional race. The tales they brought back were mind boggling. For one, there was this turn that was called the wall. I will explain. See the image below.


These bikers are cranked over to the max executing a tight turn. Look at the angle the wheels make with the ground. See the following image.


Diagram 1

This shows a schematic of a motorcycle tire when the bike is making a tight turn. If you know the coefficient of friction between the tire and the pavement, you can calculate the maximum lean angle, which translates to how tight you can turn. When the track surface is banked into the turn you can turn even tighter, lean even further, for the same coefficient of friction.


Diagram 2

At Meadowdale “The Wall” was so named because the pavement was absolutely vertical.


Diagram 3

Yes, you can ride the wall, provided you have enough traction. But what if the surface is inclined beyond the vertical, as in the next image.


Diagram 4

If you have enough traction, is it possible, in principle, for the tire to cling to the surface and support the motorcycle when there is nothing below the motorcycle but air? That is the quiz question. Post your answer as a comment below. Provide some justification for your answer, some analysis. I will post the correct answer next week, which could be as early as Sunday.


Prasad has answered the question with a “yes,” which is the correct answer.

Yes. This is in a turn only and with a sufficient speed of the bike. The centrifugal force compensates over the gravitational force.

However, he has not provided an adequate explanation. Here is a diagram that explains the forces acting on the motorcycle.


Diagram 5

The pavement curves to the right in the above diagram. This causes it to exert a rightward force on the motorcycle, diagrammed here as a tire cross-section only. Gravity acts down on the center of gravity. The frictional force acts parallel to the area of contact with the pavement. The acting forces are resolved this way.

  1. Combined gravity and friction forces produce a net CW torque on the motorcycle. The centripetal force produces a CCW torque. The two torque components cancel out, so the motorcycle does not rotate in the plane of view.
  2. The friction force contains a vertical component that exactly matches gravity. This keeps the motorcycle stable in the up-down direction. The motorcycle does not fall away from the pavement surface.


Prasad has added comments too complex to be analyzed in the comments section. I will address his comments here. First Prasad’s comments:

September 15, 2015 at 23:59 Edit

Sorry, I didn’t have the time to tackle the write-up.

However, your diagram needs a little more clarity, for lack of better words.

Acceleration is not a force. The mass of the motorcycle plus the motorcyclist does exert a force on the road surface when it accelerates but the beauty is that the motorcycle doesn’t need to be accelerating; it is just an additional benefit if you will. It does need sufficient velocity entering the turn and to counter the little friction which slows down the bike.

THE most important thing here is ‘angular momentum.’

The centrifugal force compensates for the gravity component. That is the most important thing. This does not happen in linear motion — ONLY when there is angular momentum.

The components of the forces are for students. It’s not too difficult to draw but I don’t want to draw them on a computer for lack of time.

I will tackle the various parts one at a time:

Yes, acceleration is not a force.

The motorcycle does need to be accelerating. The arrow labeled “Acceleration” in the Diagram 5 shows the direction of acceleration. Acceleration is to the right, away from the local surface. The acceleration is toward the center of the turn radius. That’s what keeps the motorcycle traveling in a circle while in the turn.

This problem has nothing to do with angular momentum. The wheels have angular momentum with respect to their turning about their axles. The motorcycle has angular momentum about it’s turn radius. Neither of these enter into the problem.

No “centrifugal force” compensates for the gravity component. The only thing that compensates for the gravity component is the vertical component of the Friction Force so labeled in Diagram 5.

Additional explanation on request. Keep reading, and stay involved.

Quiz Question

One of a continuing series

This one really is a quiz question I encountered in engineering school. We had this class on Engineering Design, and it was being taught by a Ph.D. candidate. I know his name, but I won’t reveal it. He thought we needed some stimulation, so he popped a quiz on us. “Boys and girls, here is a design problem for you.” He showed us something like the drawing below.


What you see here are two pipes running side by side, with valves. This is a schematic drawing. The pipes and valves do not look like this in real life. Those things with the Xs represent the valves. The problem, our professor told us, is you do not want both valves to be open at the same time. One valve is on, the other must be off. If you want to turn on the off valve, then you have to first turn off the on valve.

We are to design a mechanism that ensures we can perform this operation. The mechanism must ensure that it is impossible for both valves to be on at the same time.

There is an interesting story behind this, and I will tell it to you as a hint. Meaning, the solution was simple. I looked at this for about five seconds and said to myself, “Of course!” Then I drew the solution on my test paper and turned it in. I was then allowed to go about my business.

Came the next class period the professor returned our test papers, and I only received a B. How come, I asked. I provided the correct answer. How come I only got a B? The professor told me that I had obviously seen the problem before, so he could not give me full credit. This was one of those WTF moments I have experienced in college (and other times). I got an A.

Provide your answer as a comment below. You will likely need to do a drawing, so send a sketch by email. I will attach your sketch to the post. This one should be easy, so I will provide my solution on Saturday.


I’ve changed my mind. I’m going to post the answer now. People have submitted a number of worthy solutions. Here is one submitted by Michael Brown:


Nobody has come up with the optimum solution. I submit here a re-creation of my solution from 50 years ago:


Here’s how it works. Each valve stem has attached to it a disk. Each disk has a cutout that has the same radius as the disks. The valve stem on the left is constrained by stops (not shown) that limit its travel from the position shown to 90 degrees CCW. The disk on the right is constrained from its position shown to an orientation 90 degrees CCW. When the cutout is in the upper position, the valve is on. When the cutout is directed to the side, the valve is completely off.

I call this the optimum solution because no other moving parts are required besides the valve stems with their attached disks.

As I mentioned, this problem was given to us as an in-class quiz with no preparation. I had a solution submitted within 5 minutes. I had not seen this solution prior to the class period, but I had the advantage over my classmates. I had studied the mechanisms associated with motions picture film transport. I was familiar with the Geneva drive. Here it is:



The disk on the right turns. The star wheel is constrained from rotating by the machined shoulder on the disk. When the pin attached to the disk engages one of the slots, the shoulder cutout allows the pin to rotate the star wheel. The result is the star wheel shaft alternately rotates, stops for a time, then rotates again. This is what is needed to advance motion picture film during recording and during projection. This is what came to mind when I considered the problem of the two valves. The solution flowed from there. And it got me a B on the quiz.