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A Journal of Applied Mechanics and Mathematics by DrD

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Mechanics Corner

Where Would You Publish It?

Since long before my time, there has been a desire to have important results published where they become accessible to many others. Some of the great names, such as Newton, Euler, Bernoulli, and others, we know primarily because of what they published. Their work formed the fundamentals upon which modern engineering and science is built. Publication of research results has long been particularly important to faculty members; it is often taken as a measure of just how intelligent and useful they are (there is a lot of doubt about the validity of this measurement, but that has not prevented it use). When I was a young faculty member (many, many years ago), there was the mantra "Publish or Perish." This referred to the idea that those faculty members that did not publish research work would not receive tenure, and would be out of employment after several years. Agencies that funded research were eager to see publication of results that they had funded; it was considered evidence of the importance of the work supported by the agency. This was particularly true of the National Science Foundation (NSF) and other governmental funding sources in the USA.

It was not too long before publication was replaced as the measure of academic value, to be replaced by funding. A faculty member was expected to write research grant proposals, and the Dean's Office expected a significant cut of the proceeds, ostensibly for their role in "supervision." In practical terms, Dean's Offices almost never contributed anything of value to research efforts, but this was a form of graft to assure their cooperation. But publication remained essential as well. Any research that could not be published in a reputable journal was considered to be unworthy, a waste of time. So the criteria for success became, get money and publish, a tougher goal that simply publishing.

More recently, the goal posts have been moved again. Today the big cry is for "undergraduate research." To my mind, this is the height of absurdity. For folks who are just beginning to learn a profession, how can anyone think that they are capable of fundamental new discoveries? For undergraduates that are still struggling with Mechanics of Materials, do we really expect them to discover new understanding of fatigue or fracture mechanics? For a student laboring to understand dynamics, do we really expect them to come up with breakthroughs in orbital mechanics, seismic shock resistance, or multidegree of freedom models for gear box noise? But, rest assure, there is no place more insane than a university!! The utterly absurd is treated as absolutely essential!!

Thus far, I've talked a lot about academia, but we must not neglect industry. Publication is important to industrial firms as well, although for different reasons. Published research, done by your firm, is a way of establishing the technical excellence of your company. If you want to be known as an industry leader in your area, you want your employees to publish work that makes the company look like it is on the cutting edge of new technology. Often industry imposes constraints on what can be published; they do not want proprietary information to be put into the public domain. But they really like to have results published that make them look sophisticated, ahead of the pack, so to speak.

For consulting engineers, publication can be important as a means to establish your expertise in an area. If you publish a lot in a particular subject area, people begin to think you kow something about the area and come to you when they have problems. New work is the life blood of consulting engineers, so this can be very important. You will also be asked to review the work of others and to sit on panel discussions and other public appearances that can upgrade your image and bring in more work.

I hope that it is evident that most engineers will need to publish some work at some point in their career. It may be a central matter of those in more research oriented areas, or it may be only occasional for those in less cutting edge business sectors, but everyone will eventually need to publish something. So, back to the original question: Where Would You Publish It?

Most professional societies publish research work, and there are also a vast number of trade magazines. Fifty years ago, when the volume of "research" was much less, it was not too difficult to publish through any number of venues. I have published articles through the various Transactions of the American Society of Mechanical Engineers (ASME), through the Transactions of the Society of Automotive Engineers (SAE), and the Journal of Mechanism and Machine Theory. I have also published through some much less well known venues such as Machine Design magazine, and most recently through IPTEK Journal, a small journal headquartered in Indonesia (that was an experience!) and other places. But the game is ever changing!

When I first began to publish papers back in the 1960s, it was a fairly simple process. You wrote up your text, with figures and equations, and mailed it to the editor in type written form (this before the days of word processing). After a few months, you would get something back from the editor. It might be an outright acceptance (rare), a conditional acceptance which meant that the paper would be accepted with certain modifications/corrections that were described in the letter (fairly common), or it might be a flat rejection (not extremely uncommon). If you got a conditional acceptance, you made the revisions, and about 6 months later, it would be published in whatever journal you were dealing with. The classier the journal, the higher the standards were, but all worked about the same.

Many of these organizations that publish papers also hold meetings, and they want people to come to the meetings. I have presented papers at the ASME Winter Annual Meeting (always in New York), at various SAE meetings, etc. But, there is a problem. It is expensive to go to these meetings. There is the travel expense (transportation, hotel, food, etc), and there is usually an admission fee (you have to pay money to present your own paper, an absurdity, but very real). Often the papers is only accepted for publication if you agree to come to the meeting to present it and pay the admission fee. Now if your paper is the result of funded research, or if your employer will pay the expenses, this is usually not a personal burden. If neither of these apply, the burden of the costs fall of the individual, and it is often prohibitive, often approaching $1000. The publisher then sell your work for a subscription fee, usually several hundred dollars per year. Libraries are the principal subscribers (university, municipal, and industrial libraries), along with a few individual.

In recent years, there has been a glut of material offered for publication, and everybody thinks that their paper is extremely important for the world to see. The volume of publications have increased drastically, but so has the cost. Who will pay for all the paper, printing, etc.? For years, it has been common to impose what are called "page charges," typically around $100 per page, to publish in most journals. Funded research usually included a line item for page charges, so that paid those bill. In the past, any unfunded research, if it was accepted, would usually be published with the page charges waived. Today, that is not longer true, and page charges are usually mandatory. But it gets worse.

We all know the Internet is a wonderful thing, but it does have some downsides as well. One of those downsides is in the area of publication. There is a relatively recent trend in publication called "Open Access," and it is particularly popular with a number of on-line journals. These journals are free to all on the internet, but the journals charge the authors a very steep price to publish their work. Thus you, as an author, must prepare the article according some very demanding rules about formatting, style, etc, then you must pay several thousand dollars, just so the world can see your work. It means that your work becomes available to all for free (which is a good thing), but it means that you the author must bear the full cost of supporting the publishing operation. I know that I, as an individual, cannot afford this, and thus it is almost impossible for me to publish anything now. It means that those with money will get their work published, and those without money will not. The quality of the published work is virtually certain to decline, but that is modern life. What can you do?

As a closing note, I'm currently writing another technical paper that I would like to publish, preferably where folks who work with IC engines will read it. I think I have something of real value to present, but I have no idea where I will publish it, or if I will be able to find a publisher at all. If any readers have a suggestion for an appropriate journal, I would certainly appreciate a suggestion in the comments.





Where Will I Find A Job??

Where Will I Find A Job??

As I read over the questions that readers post here on ME Forum and elsewhere, I sense a common theme in many of them. There seems to be a wide, dare I say almost universal, concern about where those currently in college will find employment after graduation. To a degree this is entirely understandable; we all wonder what is in our future. Even so, the level of anxiety that I sense in many of your postings strikes me as extraordinarily high. Let us consider this a bit.

Most readers of ME Forum are currently enrolled in an engineering curriculum somewhere. Some are just beginning while others are nearing the end of their undergraduate education. I would like to pose a question to all of you: Why did you go to engineering school? Why did you choose what is probably one of the most difficult curricula in any college? For the sake of this article, I'm going to presume that I have heard at least some of your answers.

It is almost universal among engineering students to be looking forward to a good job, one that will provide them a comfortable living and a substantial measure of security. This is not at all unreasonable, and is in fact entirely probable. Almost all of you can expect to be well employed and in the upper echelons of society wherever you live. You will not rank as high as the well-known politicians, nor will you be the most wealthy people in the area. But you will have stable work and a comfortable income from that work.

What does it matter where you find employment? One of the themes I see in what I read is a great many people looking for "government jobs," that is, employment with some government entity. Traditionally, "government jobs" have been very stable. As long as a government employee stays out of trouble, in most situations it is impossible to remove that employee from his government job. This feature makes government work extremely attractive to the incompetent, to those who really cannot do the job well and thus rely on the fact that they can almost never be fired. Is this why you struggle with a difficult college curriculum, so that you can be employed with those that are incompetent? Do you really want to spend your working days with people far less capable than yourself? Many of them have achieved their positions without nearly the rigorous education that you are undergoing, so I ask you, are these the ones you want to have for your close associates?

Let me tell you a personal experience. After a long career that involved both academic positions and various industrial research positions (with a few years as a solo consulting engineer), at age 59 I took a position with a research laboratory run by the U.S. Navy. It is a sad fact of life that, in the USA, most people are considered unemployable after age 60, so I was nearing the end of the time when I could look for and expect to find a new position. The job was attractive because it promised an opportunity to do some well funded work in an area I was quite interested in, the area called electro-mechanics. The position would be very stable and I would be well payed.

In my first week on the job, I was given a few documents to read but nothing really to work on. I was not too surprised and expected all that to end very soon. After about three weeks in the new position with still in no work assignment, I began to be very worried. Every place I had worked previously had plenty of work to be done and anyone not given an assignment was probably being set up to be fired. I spoke with my boss about this several times, and he very casually told me not to worry about it. That really did not relieve my concern, particularly when he was so very casual about the whole matter. I tried to find things to work on, to make myself look useful and busy. In conversation with the other engineers, a few problems were suggested, and I worked on some of those. I wrote a few technical notes, primarily just to show that I wasn't simply sitting idle at my desk. Time went by, weeks turned into months, and months turned into years. When I finally retired from that position after seven years, I estimated that I had done at most 18 months of real work. The rest of the time I simply had nothing assigned for me to work on.

Had I realized in the beginning how the game was to be played, I would have spent my days doing things that were much more productive, such as working on problems that I found interesting, writing technical papers on those problems, and probably writing a few books. In the nonproductive 5 1/2 years I had, I could have done a lot of work! But I did not realize how the game was played, and I kept expecting someone to assign to me real engineering work to do.

As I got to know the other people, I found that a few of them had ongoing projects that were of interest to them, but most had nothing to do most of the time. I am convinced that this is the pattern of government employment, the so-called "government job." There were very few people who were truly happy in their work them: most were fairly miserable in fact. But they were wedded to the paycheck and the job security that went with their "government job." They even spoke of these factors as the "golden handcuffs." Most intended to stick it out for a total of 30 years or more, so that they could retire with a good pension.

Now I ask you, the reader, is your primary goal to retire with a good pension? Is this your principal objective in life? If so, why don't you simply roll over and die now?? While it is true that no one wants to retire in poverty, most of your life is long before retirement. Retirement is the end stage of life. I have been fortunate to live almost a decade since I retired, but it is not at all uncommon for men to die within a year or two after retirement. It seems that many simply lose their purpose in life when they retire. So to live your life in preparation for retirement is foolishness of the highest order!

If preparation for retirement is not to be your principal purpose, then what should be your objective? I submit to you that your objective ought to be to find meaningful, rewarding work in the service of other people. I am not suggesting that a group of mechanical engineers become social workers, but I am saying that you should see some connection between your work and the improvement of your society, the people among whom you live. If your work does nothing to help other people, what is its lasting value? The money you bring home in your paycheck will soon be spent. The time you invested to earn that money is already spent. So what are you contributing to mankind?

Rather than looking for a secure, comfy do-nothing "government job," I suggest to you that you should be adventurous, looking for new opportunities and new ways to help others. This is urgently needed everywhere, particularly in developing countries. Look for small startup companies with new ideas for new products, things that will improve life for everyone. Many of these companies will fail, but you are young, and looking for another job after two or three years with the company that fails is no disaster. It will not reflect badly on you if the company fails; that reflects upon the management of the company rather than upon the engineering staff. Look also at very traditional companies that are doing things the way they have always been done. Many of these companies need engineering help if they are to remain competitive and to survive into the future. This may provide you an opportunity to keep an entire company functioning, providing employment for many people. There are countless other ways that we may help our fellow man, but this should always be high in our list of priorities for the work we will do. It is while you are young that you can afford to be adventurous, to take some risks and try out things that later in life will simply be too risky. Look for challenges, situations that will require it to you use everything that you have learned, and also require you to continue to learn.

There is absolutely no point to your engineering education if your goal is simply to doze the next 50 or 60 years before you die. Plan to do something with your life, something useful, something meaningful. Do not look for a place to lay your head and simply sleep away your career.



Where is this?

Does anyone recognize where this video is shot? Is it a group of students at a school (what school?), or is it an industrial site (what company)? I am anxious for someone to locate this for me, please.



Saurabh Jain, our host, has identified this location for me, and that is much appreciated.

When I watched the video, I was aghast at all those nearly bare feet in a machine shop! I can appreciate that in Indian culture, the simple sandals are socially quite acceptable, but from a safety perspective, this is an absolute horror. Think of all the opportunities for something to drop on a foot, a tool, a machine part, sparks, etc.


Some years ago (quite a few years ago), I worked in a steel mill. We were required to wear hard hats and steel toed shoes at all times in the mill. And these were not just any old steel toed shoes. These shoes came up ankle high, and had massive steel toes and an additional steel plate, called a metatarsal plate, that came up over the top of the foot almost to the ankle. Each shoe weighed 4 lb, and it was very tiring simply to walk around wearing them. But, .... and this is the key part .... they added much to our safety. Even today, in my advanced old age, I have a pair of steel toed boots (but not metatarsal plates) for when I go into an industrial environment.


What is shown in this video is actually a cautionary tale, a warning of just about everything not to do from a safety perspective. Take heed! Be warned, or you could easily loose all your toes on one foot of the other.





What/Where to Study


I do not have the definite statistics available, but it appears to me that the majority of the readership of ME Forums is made up of students, with a much smaller number of readers at other points in their careers. By far the greatest part of these students appear to be in India, with a number in Southeast Asia and the Middle East; there are of course a few folks scattered all over the globe. It has been very interesting to me to learn about all of you, to gain an insight into your interests and concerns. I have been very surprised by a few of the things I've learned. There are two themes that stand out in my mind:

(1) there is much uncertainty about what to study, that is, what to choose for a major,
(2) where to study.

I want to offer a few comments on both of those topics in this post. Please understand that these are simply opinions, not necessarily facts. They are based upon what I think I see in the readership and in the way the world is going at large.

What to Study

Most of you are here because you have some interest in mechanical engineering. But quite a few express uncertainty about that interest. There are questions such as, "Should I switch to EE?" or "Would it be better to major in computer science?" These questions are often connected with questions and concerns about the future job market for whatever area one does choose to major in. So what can we say about such things?

It appears to me that the world economy is shifting considerably in favor of China and India. I do not think that the United States will disappear in the world economy by any means, but I do think these other two are going to become major rivals. If that is correct, the expanding economies of China and India will have a huge need for engineers and other technical people of all sorts in the years to come. It appears to me that the economies of both China and India are rapidly developing industrial economies, economies based on industrial production of goods. This would be much like the economy of the United States during the period from 1900 to about 1975. Sadly, the United States has entered a post-industrial era, also called a service economy. This does not mean that there is no industry in the US today, but it does mean that the bigger part of the economy is now based on paper shuffling, such things as banking, insurance, litigation, and fast food. The best automobiles produced in the United States today are those produced by Japanese companies such as Toyota and Honda. The machine tool industry, which was once a thriving business sector, is almost completely dead today in the US, because it has gone overseas. Almost all electronics production has moved to Southeast Asia. The production of textiles left the United States almost 100 years ago. The United States continues to have a very large agricultural industry, but that industry employs fewer people every year to produce even greater food yields. The point I hope to make here is simply that, many of you are right where you need to be to ride the crest of the rising wave of a developing industrial economy.

Many people looking at the future think very much in terms of electronic devices doing essentially everything. But I doubt that the day will ever come when we will do such things as plant crops entirely by electronics. We may use computer programs to anticipate when to plant a crop, perhaps to determine the most economically advantageous mix of crops, to help us choose fertilizers and pesticides to maximize the yield, but putting the seed in the ground and harvesting the crop will always be mechanical functions. This is simply one example but I think there are many others similar to it. There is a great future in electronics, but there is still a great future in mechanical devices as well. A growing industrial economy needs both of these and many other things as well.

Many of you seem to be concerned about the job market in the future. Will I be able to find a job as a mechanical engineer? Should I switch to computer engineering because there will be more jobs for computer engineers than there will be for mechanical engineers? These are questions that no one can really answer with full knowledge, but I can tell you a little bit. If you are really good at what you do, whether it be mechanical engineering, electrical engineering, chemical engineering, architectural engineering, etc., you will always be able to find employment. Many people look at salary surveys and say to themselves, "oh my, this year such and such a group of engineers are receiving higher salary offers that any of the others." Well, so what? When you pause to think about it, some group must always receive the highest offers, and some other group must always receive the lowest offers. That much is a mathematical certainty, but it doesn't really tell us very much.

I should add right here that if your intention is to acquire great wealth, then you should probably get out of engineering and go into business, law, or banking. That's where the big money is. Stay in engineering only if your interest is in doing something useful and meaningful with your life while earning a comfortable living. You're not likely to get rich, but I have never seen a starving engineer.

The other side of the job market concern is about the availability of jobs. We read various publications that say that X number of engineers were hired recently by Y Corporation. Depending on whether X is a large number or a small number, we think that the job market is good or that it is bad. But I would remind everyone of you that you only need, indeed can only handle, one job at a time. As long as you have a good job, one that provide satisfaction and a reasonable standard of living, there is little more you can ask for. Whether there are job advertisements for 1000 engineers or only for a few really makes no difference at all if you have a good job.

So how do you decide what to study? The answer is really rather simple. Within broad limits, you study whatever interests you. If civil engineering is really what interests you, then by all means you should study civil engineering. There will always be jobs for civil engineers. If those imaginary little things called electrons fascinate you, then you should most certainly study electrical engineering (I always enjoy teasing EEs about working with things that are not really there. I ask them how many electrons they have actually seen. I can show them a gear, a shaft, or a cam, but can they show me an electron?) There is a great future for electrical engineers. If you enjoy seeing how things move, how work gets done, how machines can make life easier for all mankind, then you should certainly become a mechanical engineer. We will always need mechanical engineers.

But there's more to this matter of "study what interests you" than simply amusing yourself. To be assured of a job, a good job, you have to be really good at your profession. There is one way, and only one way, to become really good. That is work, work, work, and then when you think you're through, work some more. During your student days, it is important that you learn everything you possibly can. You cannot possibly put in the required level of effort for the long haul if you are not studying the topic that interests you most. If you don’t know what that topic is, then you should drop out of school and only return when you have the necessary sense of direction.

Do not ask, "why do I have to learn this?" If it is presented to you as necessary course work, your response should be to dig in and learn every bit of it as thoroughly as you possibly can. You may have no idea why you need to know about this particular subject matter, but you can be pretty well assured that it would not be in the curriculum if your faculty did not think it was important. To be sure, there are a few topics that you will study and not see again for many years, but at this point in your life there is absolutely no way to predict which of those topics fall into that category. In my own case, I really did not particularly enjoy learning crystallography in the study of materials. As things have turned out, I have never needed any of that information about crystallography. But I had no way to know that when it was presented in my materials class, and in your case, crystallography may prove to be very important. During our days as students, we simply are in no position to make informed judgments about what we will need to know and what we will not need to know. For that reason, you should strive to learn everything you possibly can, in order to be the best, most versatile, most complete engineer you possibly can when you graduate. So I say again, "study what interests you" and look forward to a great future.

Where to Study

It has come as a considerable surprise to me to see the number of students who want to leave their home country to study. Many express a desire to come to the USA, or to Europe, for study. Let me deal with undergraduate and graduate study separately.

For undergraduate study, I would strongly advise everyone to stay pretty close to home. It will usually cost less money, and it will be easier in the sense that the language, customs, and overall environment will be much more familiar. To travel to a foreign land as an undergraduate can be a pretty daunting experience, one that in too many cases results in isolation, difficulty fitting into the new environment, and educational failure. None of these are good outcomes, and most can be avoided by staying pretty close to home.

In terms of quality of education, it appears to me that the Indian Institutes of Technology (IITs) are all pretty good. I have never visited one of their campuses, but I have looked at a number of videos made by IIT faculty on various engineering topics. The material covered seems to be about typical of what I would expect to see in the US. I have three principal criticisms of the IIT engineering education:

(1) The material presented seems to me to be a bit dated, that is, old-fashioned. There is continued emphasis on graphical methods of solution, to the detriment of computer numerical solution techniques. This is unfortunate.

(2) The faculty leave me with the impression that most of them are simply scholars, but very few seem to be real, practicing engineers. This comes across in the choice of example problems, in their approach to problems, and their emphasis.

(3) The faculty are, quite naturally, almost entirely native Indian nationals. This is what we would expect. But since they are teaching in English (at least all the ones I have seen), their own limited ability in English is transferred to the students. The students really need better models, so that they hear and learn from their teachers more correct English. I will say more about this in another post.

Now there may be many of you who will be quick to disagree with me, and I cannot really argue with you. I certainly have a very small sample of Indian education, but I can only tell you what I think I see.

If you were to come to the US for undergraduate study, you might be surprised to find your situation not a whole lot better. In the US, many if not most of the undergraduate courses are taught, not by regular faculty, but by Teaching Assistants (TA s). These TA s are graduate students, many from India, the Middle East, Africa, China, and Japan. The choice of material and solution methods may be a bit more up to date, but none of these TA s is a practicing engineer, and they all have linguistic limitations as well.

In short then, I urge everyone to stay relatively close to home for undergraduate study. It just make sense, I think.

For graduate study, it is a different situation. By the time you are ready for graduate school, you should be (1) considerably more mature personally, (2) more confident in your own abilities, and (3) much more ready to deal with a new cultural environment. Some problems will remain, and may be major. If you go to Germany for example, but do not know German, there will be a major language difficulty (I could not study in Germany; I know only a few, very limited, phrases in German.) If you were to come to the USA, the language would be English which you already know to some extent, but it would probably be somewhat new even so. American English is different from British English in some subtle ways, and the spoken language may be difficult for you even though you can read it well.

Sadly, in most American universities, you will find a huge emphasis on modern research ideas, and relatively little emphasis on actual engineering practice. The faculty are judged and rewarded for their research and the money that their research brings in, so naturally, that is what they tend to emphasize to their students. The world does not need countless “research engineers.” It does need a large number of highly skilled, well educated practicing engineers. But this is not where the money is for the schools, so this is not what they do.

In American universities, essentially all graduate courses are taught by regular faculty, so you would encounter the best faculty the school has to offer. You could expect to hear proper American English in the classroom all the time. You would still encounter only a relative few faculty that are actual practicing engineers (this conflicts with “research” which is where the money is).

It appears to me that a great many students come to the US to study, particularly with the hope that a student visa can be turned into a permanent visa and perhaps even eventual citizenship. Do not do this! Plan to make your home, in the long term, in your native country. The US does not need more foreign born engineers; it has plenty of native born engineers. Conversely, most of your countries have a great need for excellent engineers, people who can contribute to the economic and social development of your country. The very best people to do that are the ones born there. You can do that far better than I could. If I were to go to India, for example, I might be able to help some, but not nearly as much as you can. I would not know the customs and the culture, the languages, or the history like you do. Whether you do graduate school at home or abroad, plan to return home for the long term. That is where you can do the most good for mankind.


To sum up then, I recommend undergraduate work near your home. Graduate work may continue there, or abroad, but your goal should be to return to your home to make your career there. Be sure to study the topic that really interests you, and pay little or no attention to employment or salary surveys. You only want one job, and it will be there for you if you are really well prepared.


War Stories


Mechanics Corner
    A Journal of Applied Mechanics and Mathematics by DrD
    © Machinery Dynamics Research, 2016

War Stories -- Dr. Jack Levedahl

Today I want to tell a few war stories, war stories in the literal sense of the word, in that they all relate in one way or another to World War II. They all center on my friend Dr. Jack Levedahl, a most excellent mechanical engineer and adventurer. Jack was an elderly man when I first met him about 15 years ago, and he has since passed on, but I remember him with great fondness and respect.

Jack grew up in a Swedish American family in Aurora, Illinois, southwest of Chicago. He grew up hunting small game in the fields around the town and tinkering in the machine shop his family ran. At the time that World War II began for the US, Jack was a mechanical engineering student at MIT. When the US entered the war, Jack dropped out of college and joined the US Army Air Force, as it was then called. Jack became a pilot and flew the North American P-51, the finest propeller driven fighter the US has ever built. The P-51 was originally designed for an American-made Continental Lycoming engine, but that didn't have enough umph! It wasn't long before the design was revised to include a Rolls-Royce Merlin engine with about 1600 hp. This gave the P-51 a top speed of around 450 mph, the fastest mass produced aircraft of WW II. It was quite a excellent machine!

The Merlin engine was a marvelous design, but it was not easy to build. In England, the Brits built these engines one-by-one, essentially by hand, hand fitting all the bearings and other precision parts. There was simply no possibility that Rolls-Royce could supply engines at the rate needed by the US Army Air Force. For that reason, the design was licensed to the Packard automobile company in the US. Packard engineers reworked the design, loosening tolerances wherever possible, and came up with an engine that could be mass-produced. This produced an engine that was in many ways superior to the handmade engines from the UK. The Rolls-Royce engines were like a fine watch, but they had practically no truly interchangeable parts. This made field repairs extremely difficult and time-consuming. The Packard built engines ran a little more noisily, but they all had fully interchangeable parts and could be repaired with ease. This last proved to be a great benefit in the theater of war.

When Jack had completed his training, he was sent to the Mediterranean where he was based on Sicily, flying missions north up the Italian peninsula. Gradually the Allied effort was driving the Germans back, and they were retreating back toward Germany. Jack told me in some detail about one such mission.

Jack said that he and his wing man were attacking a German train headed north through the Brenner Pass into Austria. This was not an ordinary train but rather was an armored train. It carried on board a number of antiaircraft cannons, capable of firing at attacking aircraft. As they bored in on the train, Jack said his wing man was hit and went down, but he got through and shot-up the locomotive, causing the boiler to explode.

I visited Jack in his apartment in Annapolis, Maryland one day where I saw a strip of aluminum about 15 inches wide and about 7 feet long hanging over a wide doorway. It was literally torn to pieces, with large gaping holes gouged through it, rather clearly the work of large bullets (probably 30 mm cannon fire). I asked Jack what the piece of metal was. He replied, "Oh, that was the canopy fairing from my plane. That was right behind me in the cockpit." When he had returned from one of his missions with his plane shot full of holes, the aircraft mechanics had salvage this one piece for him for a souvenir. When I asked if there had been anything else between him and the bullets he explained that there was an aluminum armor plate, about 1/2 inch thick behind his seat and that was all.

When he had completed 50 missions, Jack was mustered out of the Army Air Force, even though the war was continuing. He did not want to leave, but there was a rule that if you survived to complete 50 missions you had to be retired. Not too many pilots survived 50 missions, so it wasn't a problem for very many people. Reluctantly, Jack returned to the US and enrolled again in MIT where he finished his degree. He went on and got a master's degree as well.

Jack told me that one day about 1947 or 1948, he encountered a German-speaking man on the streets of Milwaukee, Wisconsin. The man was asking, in German, for directions to Mader’s, a famous German restaurant in Milwaukee. Jack spoke some German and was able to communicate with him, so he walked the visitor a few blocks over to the restaurant where they had a meal together. It turned out that the visitor was a famous mechanical engineering professor from the University of Aachen in Germany. He invited Jack to come to Aachen to study with him, and that's where Jack did his doctoral work.

During the time that he was studying in Germany in the postwar period, Jack said that many of his fellow students were former German army personnel. One day, in a graduate student bull session, one of the other students described what he had done during the war. He explained that he had been a gunner on an armored train. He said that all came to an end one particular day in the Brenner Pass when his train was attacked by two American P-51s. He went on to say that he had shot down one of the attacking aircraft, but the other one got through and destroyed the locomotive of his train. It was a bit strange for Jack to have to tell him that he was the one who got through and blew up the locomotive!

For many years after the war Jack was a research engineer for the U.S. Navy, working on a variety of projects. It was in that capacity that I encountered him when I worked for the U.S. Navy in a similar situation at the end of my working career. The Navy had a program for its research personnel that was called "Scientist-to-Sea" in which research engineers were allowed to sail on US naval ships under certain circumstances. Jack and I signed up for one of these cruise opportunities, and we sailed together from New York harbor down to Pascagoula, Mississippi on the destroyer Roosevelt, DDG-80. It was a marvelous eight days at sea, and we were free to explore the ship from stem to stern, talking to anyone and everyone and asking any question. So imagine two elderly men, acting like two kids, roaming the ship and asking to be let into out-of-the-way places such as the chain locker for the anchor chain and the steering gear compartment at the stern of the ship. We would go together and look in a section of the ship, and then we would return to the state room that we shared. There we would discuss what we saw, and frequently disagree about exact details of what we had seen. When we disagreed, we would get up and return to that part of the ship to take a second look, and thrash out just how each ship system worked. It was a grand experience for me, to be able to explore this fascinating mechanical system called a destroyer and continually discuss parts of it with this highly experienced and vastly knowledgeable mechanical engineer. I miss him greatly!


The following is a verbal description of a Doonesbury cartoon of unknown date by Garry Trudeau. Doonesbury has long been one of America’s major cartoon strips, with a very dry wit and a decidedly left-of-center outlook. I found this today in going through some old files.

SCENE: A college classroom, the teacher lecturing in a rather absent minded fashion, the students silently bent over, taking notes and keeping their heads down.

TEACHER: Of course, in his deliberations on American capitalism, Hamilton could not have foreseen the awesome private fortunes that would be amassed at the expense of the common good.

TEACHER: Take the modern example of the inventor of the radar detector. In less than ten years, he made $175 million selling a device whose sole purpose is to help millions of people break the law.

TEACHER: In other words ...

STUDENT (suddenly sitting up and interjecting): Maybe the fuzz buster is a form of Libertarian civil disobedience, man. You know, like a blow for individual freedom.

TEACHER: I ... I don’t believe it!

STUDENT: Believe what, man?

TEACHER (smiling in happy elation!): A Response! I finally got a thinking response from one of you. And I thought you were all stenographers! I have a student! A student LIVES!

TEACHER (kneeling down, hand extended like one might approach a shy animal): Who are you lad? Where did you come from? Don’t be frightened ...

STUDENT: (looking around himself): What’s the deal here? Am I in trouble?

The above all appeared in print many years ago, but it is an apt description of Mechanics Corner.


Value Engineering

A toothpaste factory had a problem.  They sometimes shipped empty boxes, boxes without the tube inside. This challenged their perceived quality with the buyers and distributors. Understanding how important the relationship with them was, the CEO of the company assembled his top people. They decided to hire an external engineering company to solve their empty boxes problem. The project followed the usual process: budget and project sponsor allocated, RFP, and third-parties selected.  Six months (and $8 million) later they had a fantastic solution - on time, on budget, and high quality.  Everyone in the project was pleased.

 They solved the problem by using a high-tech precision scale that would sound a bell and flash lights whenever a toothpaste box weighed less than it should. The line would stop, someone would walk over, remove the defective box, and then press another button to re-start the line. As a result of the new package monitoring process, no empty boxes were being shipped out of the factory.

With no more customer complaints, the CEO felt the $8 million was well spent. He then reviewed the line statistics report and discovered the number of empty boxes picked up by the scale in the first week was consistent with projections, however, the next three weeks were zero! The estimated rate should have been at least a dozen boxes a day. He had the engineers check the equipment, they verified the report as accurate.

 Puzzled, the CEO traveled down to the factory, viewed the part of the line where the precision scale was installed, and observed just ahead of the new $8 million dollar solution sat a $20 desk fan blowing the empty boxes off the belt and into a bin.  He asked the line supervisor what that was about.

 "Oh, that," the supervisor replied, "Bert, the kid from maintenance, put it there because he was tired of walking over, removing the box and re-starting the line every time the bell rang.”


Mechanics Corner

A Journal of Applied Mechanics and Mathematics by DrD, #40

July, 2017


Two Short Math Problems

Do you ever read the ads that appear on ME Forum? I try to avoid them as much as possible, but an organization called BRILLIANT has put up some interesting math problems of late that have caught my eye. Two of them are the subject of today's post.

The first problem that I want to discuss is actually more recent than the other, but it gives us a good place to start. Following that, we'll go on to the second problem. Along the way, I want to talk about philosophy as well as simply how to solve tow specific problems. The main lessons to be learned here are in regard to how we use mathematics in the practice of Mechanical Engineering.

40 Two Short Math Problems.pdf



Mechanics Corner
    A Journal of Applied Mechanics and Mathematics by DrD, # 37
    29 April 2017

Two Balls Rolling On An Incline
A Problem Where I Learned Something New


    In previous articles, I have mentioned another web site called Physics Forums (PF) where people post problems for which they need help. In this note, I want to present to you one such problem and it solution, along with a new insight that came from another commenter at PF, one of the advisory folk on that site. At first, I thought the adviser was wrong, but it turns out that he was correct and had something new that I had never seen before. Here is the problem.

Problem Statement

    A thin wall spherical shell with a mass of 0.605 kg and a radius of 0.0402 m is released from rest at the top of an incline. The spherical shell rolls down the incline without slipping. The spherical shell takes 7.49 s to get to the bottom of the incline.
    A solid sphere with mass of 0.127 kg and a radius of 0.1123 m is released from rest at the top of the same incline. The solid sphere rolls down the incline without slipping. How much time does it take for the solid sphere to reach the bottom of the incline.
    Note that ---
Thin spherical shell        I=(2/3)MR^2
Solid sphere        I=(2/5)MR^2



    The original problem statement is above. Note what is given, and perhaps more importantly, what is not given. In particular, we are not given

1.The time for the solid sphere to reach the bottom -- this is the item to be determined;
2.The angle of the incline;
3.The length of the incline;
4.The local value of g, the acceleration of gravity.

    The last three items are things that we might expect to have given in such a problem, but here they are not. This is the major difficulty in this problem, and the solution must find a way to work around this missing information.



Twenty One Rules for Tech Writing


One of the things that has surprised me about the readers of ME Forum is the number of folk who want to publish technical papers. When I was an undergraduate (a very, very long time ago), publishing papers was the farthest thing from my mind. I knew that publishing was a concern for some of the faculty, but it was certainly no concern of mine! To my even greater amazement, most of those desiring to write want to write in English, even though this is not their mother-tongue. I presume that this is a natural consequence of the fact that English has come to dominate the technical literature world-wide. That is a good thing for me (I only speak one language), but I would think it must be a daunting prospect for many of you. I have great respect for anyone who would undertake to write a technical paper in a foreign language; it is quite enough of a challenge in a language that I know pretty well. But perhaps it is not so much “foreign” as it is simply a “second language,” for those of you that know multiple languages. Either way, I am impressed that you would tackle this difficult undertaking at this point in your lives.

The purpose of this article is an attempt to help those of you who wish to publish, particularly technical publications. Most of what I have to say can be applied to anything you write, comments about such matters as organization, for example. Other parts of this article apply specifically to publication in technical journals, so you must use my suggestions with understand as to where they apply and where they do not.

I am organizing this article in two main parts. The first part I have labeled as Philosophy, meaning that it provides some guiding principles to be kept in mind about the way you construct your paper. The second part is labeled Mechanics and refers to details about actual construction of the paper. You will find that both of these are important. I have been reviewing papers for many years now for ASME, SAE, Journal of Mechanism and Machine Theory, and others, and I can tell you with certainty, that many papers fail on some of the most mundane items discussed here. These things matter, and if you want your paper to be accepted, you will need to pay attention to them all.


1. Have something interesting to say. There is simply no point to attempting to write a paper on an uninteresting topic, one that does not interest you, the writer, nor the reader. There are times when it is necessary to report information that is less than fascinating, but as the writer, you should seek to find what there is about this information that is interesting and/or important to the reader and point that out. You should never choose to write on a topic where you really do not know what you are talking about; it just will not work!

2. Identify your reader. In most cases, you will not know exactly who the reader is going to be, but you should have some pretty clear ideas about him nevertheless. You will be making definite assumptions about the reader (it may be helpful to go so far as to write these out), about his background and preparation for what you are going to present. Are you writing for a broad, general audience with a limited technical background, or are you writing for someone who is a specialist in the field and perhaps has even more background than you do? The assumptions you make about the reader will have a major impact on what you say and how you say it, so it is necessary to be rather definite about the capabilities of the reader.

3. Identify your publisher. When you write, you need to keep in mind who will be publishing your work. Most established publishers have very definite requirements regarding style, page layouts, footnote/endnote requirements, and a host of other matters. Many journals will publish in each issue a short section with a title like “Information for Authors,” and today this will usually lead a link for a URL where you will find pages and pages of detailed requirements. It is better by far to be aware of these requirements before you begin writing rather than having to do major re-writing simply to meet the publisher’s requirements.

4. Organize your story in a logical form. This is often not the way things came first to you, but it is necessary to make things easy for the reader. Think about the easiest possible way to explain your subject to a reader, the sequencing of information that will enable him to most easily understand the whole topic. This will help you to keep your paper concise and focused.

5. Provide any necessary background. This is often done in an Introduction where you survey related previous work so that someone not intimately acquainted with the field can still follow your work. Depending upon the nature of the publication (journal article, technical report, lab report, etc.),  a bit of basic review may be appropriate in some situations.

6. Use correct terminology. Terms such as axial, radial, height, width, length, vertical, horizontal, cylindrical, conical, spherical, etc. have rather specific universal meanings. Be sure to describe carefully the orientation of dimension, and other similar matters that are often essential for a clear understanding. Consider the four words: depth, height, width, length. What directions are associated with each? Height is usually vertical, that is aligned with the local gravity vector. The length of something is usually the longest dimension, assuming that this dimension is horizontal, but what happens if it is not horizontal? The word depth is sometimes associated with a vertical distance, such as the water depth, but it is also associated with a horizontal distance measured away from the observer. The ambiguity of these words means that they must be used with great care. Often it is necessary to say something like, “The depth of the hole, measured in the horizontal plane, is ...” or “The width is 42 mm, as shown on the drawing.”

7. Use consistent terminology throughout. If you call something a brick at the beginning, then it must be called a brick throughout. If you start off talking about the engine, do not switch to talking about the motor. The exception to this occurs when you use a common place term to introduce an idea before giving the technically correct term. Consider for example, “The longest edge of a right triangle is called the hypotenuse.” The common term in this example is “longest edge,” but the technically correct term is “hypotenuse.”

8. Use figures, but use them sparingly. Figures can add a lot of interest to your publication, as well as conveying much information in a simple, easy to understand form. But remember that they are there to inform, to carry information from you to the reader, not simply to look pretty. They take up a lot of space, so they must convey a lot of information. On the other hand, they must not be too cluttered, with text too small to read. Labels with leader lines can help in many cases.

9. Always write a conclusion. The conclusion is important to solidify in the mind of the reader what it is that he has just read. When you write your final conclusion, be sure that your text supports everything that you are concluding and that you have told the whole story.

10. Don’t make you paper too long. Most journals impose a limit of 8 pages, including figures and references, so be concise. There are exceptions, journals that allow longer papers, but the best ones generally have a firm limit. If a paper becomes too long, the reader is very likely to loose interest before finishing, in which case, you have not reached the reader with your information and he has wasted his time.


11. Be precise in the use of words. Don’t describe everything as “efficient,” when you really mean “more effective,” “faster” “less expensive,” “more aesthetic,” etc. The bigger your vocabulary is, the easier this will be. Avoid “engineer–speak,” that is, the sort of slang that engineers often use on the job, such terms as “down-force,”  “up-draft,” “bhp,” “mip,” “CG,” “cross-over,” etc. (Does everyone know that the CM and the CG are usually the same location, although not always? Giving the whole term makes clear which you mean.) If you think they are necessary, then you must define them in the text. In this same vein, for technical publications it is never acceptable to use the abbreviated form that have become popular with instant messaging, texting, Twitter, etc. I am speaking about such things as “u r” for “you are,” “b4” for “before,” and similar extreme contractions of words.

12. Number all figures, and provide a title. In so far as possible, all figures should be uniform in style. Think twice about the use of color. It looks pretty when well reproduced, but will it always do so? Multi-color figures on a black and white copier lose most of their information. For most purposes, black lines on a white background are the best idea.

13. Number all pages. This seems obvious, but evidently it is not so to everyone. This helps put the pages in order if they get shuffled, it helps a reviewer refer to specific items, and it helps a reader to locate information given in a citation.

14. Number all equations. Again, this seems obvious, but not so to everyone. Use conventional symbols wherever possible (Greek rho for mass density, W for weight, m for mass, v for velocity, etc.) For journal publication, do not show substitutions of numeric values into an equation. Instead, solve the equation in symbols and then show the final numeric result. There may be an exception when for a professional report (such as a stress analysis for a client), you may need to show the substitution.

15. Provide section and subsection heads. This helps to give structure to your paper, conveying the logic of your presentation. Also, it suggests to the reader where to look for particular information.

16. Start a new paragraph with each new idea. The basic purpose of a paragraph is to present one, and only one, idea. This is true even for summary paragraphs where the new idea is the interrelatedness of several ideas presented previously. Single sentence paragraphs are to be avoided.

17. Use spell-check. With all the word processing capability available today, almost all of it including a spell checking feature, there is absolutely no excuse for misspelled words. Now spell-check will not check the logic of your sentences, so the simple fact that spell-check did not flag anything does not mean that everything is correct. But if spell-check does flag a word, you must correct it.

18. Punctuate and capitalize correctly. Be sure to single space after a period at the end of every sentence. When using a hyphen to break a word, do not include a space. Punctuate consistently throughout, with the publisher’s rules as your main guide. Above all, be consistent. It looks terrible to see a space on one side of a hyphen and not on the other

19. Use consistent units throughout, usually SI. This would seem to be obvious, but it is not so to everyone. Most of your work should be formulated in such a way that it is units-free, that is, so that it may be used with any consistent system of units. But when you are reporting numerical results, you will have to use units (unless you use dimension-less ratios which are not entirely satisfactory).

20. Use abbreviations correctly.  If you want to use an abbreviation, such as BWR for Boiling Water Reactor, the whole thing must be spelled out the first time, with the abbreviation immediately following in parentheses. Thus, we might say, “Westinghouse provided the Boiling Water Reactor (BWR) for the installation.” Thereafter, use BWR consistently, except at the beginning of a sentence (do not start with an abbreviation).

21. Proof-read, proof-read, proof-read! Putting the words into the computer is only the beginning of writing a paper, definitely not the end. It is necessary to proof read, looking for many different potential problems. Does every sentence make sense and say what you intended for it to say? Is your explanation complete, or are there gaps in it? Is the punctuation and capitalization all correct? Have you followed the publisher’s guidelines for format, style, equation numbering, etc.? When you have read it and re-read it many times, to the point that you think it is perfect, then get someone else to proof-read it also for you. The failure to adequately proof-read is one of the most common of failings, and it reflects very badly on the author. It says that the author did not think that this article was worth making perfect, which makes the reader wonder why he should bother with it at all?

Following these rules does not assure that your paper will be accepted by one of the leading journals of the world, but failure to follow them virtually assures that your paper will fail. The whole idea of writing a paper is to communicate something to a reader, and these rules are largely about steps that you, the author, can take to facilitate that communication. If what you say is not interesting or is unclear, then there will be no communication. These rules are all about clarity and ease of communication.




Triple Rocker

Mechanics Corner

A Journal of Applied Mechanics and Mathematics by DrD

July 31, 2017

Triple Rocker

Over at the Kinematics of Machines club, I recently ask if anyone could show me an example of a four-bar linkage that would be classed as a triple rocker. In the terminology of four-bar linkages, a link is classed as either a crank or a rocker:

Crank - can rotate in a complete circle

Rocker - cannot rotate in a complete circle]

Thus my question was for an example of a four-bar linkage where no link is able to rotate around a full circle. My request has not generated any answers, but fortunately, I stumbled onto one.


Since the definition of a rocker is a link that cannot rotate completely, it is evident that the linkage shown is in fact a Triple Rocker. None of the links is able to move through a complete revolution. If we try to rotate the input (left) link further down, it cannot happen without stretching the combination of the coupler and the output (right) links. When the input link (left side) gets to the top, again its motion is stopped by the need to stretch the coupler and output link. Thus, a figure I drew as an illustration for something else turns out to be a Triple Rocker, the item I was looking to find.

In connection with four-bar linkages, some readers will have heard of Grashof's theorem. Let

s = length of shortest link

L = length of the longest link

p, q = lengths of the two intermediate links

Grashof's theorem says that a necessary and sufficient condition for at least one link to be a crank (able to rotate entirely around), it is necessary that

s + L < p + q

This inequality is not satisfied for the four-bar that I drew by chance, so Grashof's theorem says that none of the links can be a crank. That is precisely the condition required for a Triple Rocker (a ground link plus three moving but not fully rotating links). So, there you have it. That is an example of a Triple Rocker, and we now have the criteria for identifying such as a four-bar linkage that does not satisfy Grashof's Theorem.




Mechanics Corner
 A Journal of Applied Mechanics and Mathematics by DrD, # 22
(c)  Machinery Dynamics Research, 2016

Torsional Stiffness of a Shaft -- Part I
    A shaft is a common machine element, used to transmit rotational motion and torque from one component to the next. It is clear that the length of the shaft must be sufficient to span the distance from the first component to the second, but what should the diameter be? The answer to this question requires first answering two related questions:
  -->  How much torque is to be transmitted? This will define the strength requirements for the shaft so that it does not fail under load.
  -->  What stiffness is required for the shaft? This will determine the angular relation between the two ends of the shaft, important in cases where angular displacement accuracy is a concern and also a major factor in the torsional vibrations of the system.
    As is typical with a design problem, the designer is not able to simply specify what is required and compute the required dimensions. Rather, it is necessary to propose a design, that is, to propose both shape and dimensions, and then see if the strength and stiffness requirements are met by the proposed design. There are many possible designs for a shaft, so it is important to deal with the necessary stiffness calculations for a variety of geometries (the matter of strength is left to another time).
    The basic theory required for this work is commonly found in all Mechanics of Materials textbooks (see for example, Timoshenko). There are also two well known references that deal specifically with this material. The first is the BICERA Handbook (which is the source for many of the ideas in this note) and also the work of Wilson.




Mechanics Corner
    A Journal of Applied Mechanics and Mathematics by DrD, # 24
    © Machinery Dynamics Research, 2016

Torsional Stiffness of a Shaft -- Part III

    The discussion in previous parts of this series has focused on stiffness (or compliance) estimates for various shaft geometries. There has been nothing said yet about joining parts together, although most readers will readily agree that integral (single piece) shaft assemblies are very rare in practice. It is time to discuss joining multiple components together to form a shaft system.
    The list of possible coupling types is almost endless, so this article will simply focus on a few of the more common types to illustrate the thought processes.

Keyway or Spline

    Before considering actually joining to a second member, if the connection is to be made by means of a key or a spline, it is appropriate to look at the way in which the keyway (or spline) itself increases compliance in the section where there is no torque transfer.


    [Fig. 1  Shaft Sections with Keyway (left) and Spine (right)]

    Where a key is used, the keyway is usually cut significantly longer than the key itself. This results in a section of the shaft that effectively has reduced diameter. Experience has shown that this can be treated adequately by considering it to be a uniform solid shaft of diameter Deff as shown in Fig. 1.
    Similarly, where a spline is used, it is not difficult to see that the ribs that form the spline teeth carry no significant shear. Thus the part of the shaft that is splined is also properly modeled as a uniform solid shaft with diameter Deff as shown in Fig. 1.




Mechanics Corner
    A Journal of Applied Mechanics and Mathematics by DrD, # 23
    © Machinery Dynamics Research, 2016

Torsional Stiffness of a Shaft -- Part II

    In the previous post of this series, a variety of shaft forms involving both solid and hollow sections were considered. A general approach was developed, applicable to various sorts of non-uniform shafts, but always subject to the provision that the variation in section was gradual; no sudden changes in section were permitted among the forms considered. This leads directly to the question that is the focus of this post: "How are sudden changes in diameter taken into account?" Steps, also called "shoulders" are a common feature of many shaft designs, used to locate rotating elements (fans, flywheels, pulleys, etc) on the shaft. They are also used in connection with bearings and seals. It is important that the means be established to account for shoulders in the shaft stiffness calculations.

Compliance of a Stepped Shaft

    At typical shaft section involving a step or shoulder is shown in Fig. 1. As usual, it is assumed that all of the dimensional data is known. The difficulty is the rather abrupt step from diameter D1  up to D2 . For the development below, it is always understood that D1 < D2. By the methods previously established in Part I, the compliance of each shaft segment can easily be computed,




The VEProject --- Shifted Levers
A Critical Assessment



    The subject of this article is the VEProject Shifted Lever video, as found at the following URL:

    The video shows a "Shifted Lever" mechanism, a device that appears to be perpetually off balance. It is presented as a perpetual motion mechanism, that is, a machine that will run forever without any energy input other than, perhaps, an initial push. This presentation comes from the VEProject, where VEProject stands for "Visual Education Project." An educational project can be presumed to be a presentation of truth, so should we accept that the author believes that this device is truly a perpetual motion device, or that he is attempting to deceive the viewer?
    As most Mechanical Engineers know, the laws of thermodynamics show that there cannot be perpetual motion. So, are the laws of thermodynamics incorrect, or are we being deceived?



1. Team building is very popular in industry these days, so here is a team building joke.

A group of mathematicians are attending a weekend seminar on team building. During the night, a fire breaks out in the room of one of the mathematicians. He quickly tears pages out of his notes and lights them on fire, one by one. He then runs down the hall, shoving burning sheets of paper under the doors of all the other mathematicians.

In the morning, after the building is burnt to the ground, the fire marshal asks how the fire spread so fast. The initiator spoke up and said, "I thought distributing the problem would lead to a quicker solution."

2. Summary of the important laws that MEs must know:

From statics,  Stuff does not move on its own.

From dynamics: Stuff fights back (Newton's 3rd Law)

From mechanics of materials: Stuff stretches and breaks (Hooke's Law)

1st Law of Thermo: You can't win.

2nd Law of Thermo: You can't break even.

3rd Law of Thermo: You can't stop playing.

Addendum: Entropy isn't what it used to be.

3. An engineer, a physicist, and a statistician go hunting together. When some game is sighted, the physicist calculates his trajectory using ballistic equations, but omits air resistance. His shot falls 5 meters short. The engineer adds a fudge factor to compensate for air resistance, but his shot fall 5 meters long. The statistician shouts, "We got 'em!"

4. An engineer and a physicist are lost in a hot air balloon drifting along. The physicist is busy trying to use sextant to determine their position when the engineer spots someone on the ground. The engineer yells, "Where are we?" The man on the ground calls back, "You are in a hot air balloon, 100 ft above ground." The engineer and the physicist look at each other and one says, "That man is a mathematician. His answer was entirely correct and completely useless."

5. There is a calculus party and all the functions have been invited. ln(x) is talking with some trig functions when he see his friend e^x sulking in a corner. He says, "What's wrong, e^x?" e^x replies, "I'm lonely," to which ln(x) replies, "You should try to integrate yourself into the crowd." In despair, e^x cries out, "It won't make any difference at all!"

6. If you can just remember all these jokes, you will be a hit at the next of those parties you imagine yourself being invited to.





Rocket Homework Problem

    Mechanics Corner
    A Journal of Applied Mechanics and Mathematics by DrD, #38
      Machinery Dynamics Research, 2017


Rocket Homework Problem


    Most engineers find problems involving rockets to be exciting. There is something about a rocket that fires our imagination, whether we think of going to the moon or one of the planets, or simply of shooting down an incoming missile. The subject of this post involves a rocket on a mobile launcher. The rocket is intended to be transported in a horizontal position, but it must be elevated in order to be fired. Both positions are shown in the accompanying figure.

Read the attached PDF for more on this problem.



Addendum:  One reader has posted a proposed solution for this problem as a comment. It was not my intent that solutions be posted in the comments at all. I only want solutions sent to me by the personal message system. DO NOT POST YOUR SOLUTION IN THE COMMENTS!!

Regarding the solution that has been posted, let me say the following:

1. Some of the answers are correct, while others are not. Do not be misled into following this solution because there are errors therein.

2. Even where the results are correct, there are a number of methods that I would not recommend using. Thus again, I say to all other readers, do not follow this solution, but work it out for yourself.

3. Be sure to document your solution, so that if someone else were to ask how you obtained a particular result, you would be able to explain it in a clear and reasonable manner.





Puzzled (A Poll)

The response here at Mechanical Engineering Forums, or should I say, the lack of response, has left me puzzled. There was a modest response (as indicated by comments) to my first post, but the number of comments has dropped to almost nothing since then. I am only aware of one person who has actually worked on one of the challenge problems that I have posed (but I hope that there are more who have). In the previous poll, there have been a good number of views, but an extremely small number of people have answered the poll. What does this all mean?

There are a lot of possible interpretations. Is the material too difficult? Is the material too simple? Are the topics boring? Are the topics too general? Is the application of these ideas not evident? Do you want to see more problems carried through to numerical answers?

Would you like to see more articles on other topics, such as (1) vibrations, (2) stress and deflection analysis, (3) gears, (4) cams, (5) electromechanics, (6) applied mathematics, (7) computer methods?

Would you like to see more articles on specific applications, with the presumption that you already know all of the necessary back ground? I’m thinking, for example, of an article I intend to write eventually about a vibration attenuation system. In order to understand that article, the reader is going to need to have a general background in multi-degree of freedom linear vibrations. Are all readers ready to simply jump into that subject?

Please answer the following poll questions, and add your comments on this topic at the bottom. I am most interested in your feedback.



    Mechanics Corner
    A Journal of Applied Mechanics and Mathematics by DrD
      Machinery Dynamics Research, (c)  2016

Professional Societies -- Or Not?

    This post is written in response to questions raised by one of our regular participants, a young engineer in Australia. What I have to say here is based entirely on my own, very American, experience, and others may have different ideas. I would encourage a general discussion in the comments, so that we may see how various folks look at this question.
    The questioner asked, "... have you maintained a membership to such an organization for the purposes of networking and staying active in the engineering world?" I'd like to re-word the question just slightly to read, "What is the purpose for being in a professional society, and is it worth the costs?" My experience in this matter is limited strictly to American professional societies, but I suspect there will be some carry over to other nations as well.

What are we talking about?
    Before getting into the good and bad points, it is worthwhile to cite some examples of various professional societies, so that everyone will understand the kind of organizations are under consideration. Let me name a few that come to mind, just off the top of my head:
    ASME --- The American Society of Mechanical Engineers
    SAE --- Originally called the Society of Automotive Engineers, now legally simply SAE
    ASHRAE --- American Society of Heating, Refrigeration, and Air-conditioning Engineers
    NSPE --- National Society of Professional Engineers
    ASNE --- American Society of Naval Engineers
    SNAME --- Society of Naval Architects and Marine Engineers
    AIAA --- American Institute of Aeronautics and Astronautics
    IEEE --- Institution of Electrical and Electronic Engineers
    SME --- Society of Manufacturing Engineers
    ASCE --- American Society of Civil Engineers
    AIChE --- American Institute of Chemical Engineers
    IIE --- Institute of Industrial Engineers
    SAME --- Society of American Military Engineers
    SPE --- Society of Petroleum Engineers
    AWS --- American Welding Society
    This list is certainly not exhaustive; there are many more such organizations. As this brief list suggests, there is an organization for every interest! Let me talk a little bit about a few of these, the ones of which I am a member and one other that I am familiar with.

    In many respects, ASME has long been the premier mechanical engineering society in the US. It first rose to prominence in the early 20th century when there was a nation-wide problem with boiler explosions. ASME took the lead in developing boiler standards, and today the ASME Boiler and Pressure Vessel Code is recognized world wide as a guide to safe design of such systems. Sales of the Code documents are a major source of income for the organization, and ASME is very active in many areas of Codes & Standards. It also published a number of technical journals, such as the Transaction of ASME, Journal of Applied Mechanics. They also organize and host many conferences around the country, and indeed around the world, on various topics of specialist interest.
    When I first joined ASME as a student in the early 1960s, it was a very membership oriented organization. Each year, when you paid your dues, you received five coupons that could be redeemed for technical papers that were available from ASME. At that time, the membership really ran the organization. Today, it has all changed. It is simply a business, run by a bunch of folks in New York, for their own benefit, and they simply do not care about the needs of the membership. If I want an ASME paper, I can buy it for about $25, exactly the same as anyone else can get it. There are ASME Student Sections at most American engineering schools, but ASME does little or nothing to support them. Over the years, I have attended many ASME functions, from local section meetings to national conferences. They are often well attended, and they are an opportunity to meet others in the field.
    I am a Life Member of ASME which simply means that I was foolish enough to pay dues for 30 years, and now I am exempt from further dues. I probably would not join ASME if I were starting today with what I know now.

    SAE was originally known as the Society of Automotive Engineers, a fairly self-explanatory name. It has dropped the name to become simply SAE, and refers to itself as "the mobility society." It incorporates folks interested in mechanics, materials, fuels, lubricants, combustion, controls, electronics, etc., and deals with automobiles, trucks, ag machinery, boats, and aircraft. It is very, very broad, and almost any technical person can find a role in SAE. SAE, like ASME, also publishes many Codes and Standards, and organizes a number of technical meetings each year.
    One thing that I think is important about SAE is the way it supports engineering education. SAE sponsors, with significant amounts of money, many student design competitions in which undergraduates design, build, and test various real projects. One of the most popular of these is what is called the Mini-Baja Competition, a reference to the famous off-road racing done in Baja California (Lower Califormia, Mexico, a very primitive area located directly south of the US state of Califormia). Let me tell you a bit more about my own involvement with SAE.
    In the mid-1980s, I was teaching in a small engineering school in Wisconsin. I was in my office one afternoon when one of my former students burst in, eager to talk to me. Brad said, "Are you a member SAE?" to which I replied, "No, I am a member of ASME." He came back with "Well, would you be?" which really puzzled me. Why did he care whether I would join SAE or not? As the whole story came out, he was nearing graduation, and he wanted to do something of lasting value for the school. His idea was to organize a SAE Student Chapter and get them involved with the Mini-Baja race car competition. Such a group would need a faculty adviser, and he wanted me to be that adviser. To make a long story short, I joined SAE and we got approval to organize a Student Chapter and got started on the construction of a race car. I was amazed at the student enthusiasm, and also at the financial support we got from the Senior Section (the adult SAE Section in our area). Money poured in from the Senior Section, and we received a donated engine (everyone uses the same engine) and many items of donated hardware. We did not win that first year, but we did the next year, and I'm proud to say, the group continues to this day, doing very well year after year! A couple of years ago, I attended an SAE student competition where they were racing Formula I race cars. We had about 25 schools represented, coming from as far as 1000 miles away for the competition! This is a serious boost for engineering education, and a real service!

    SNAME is the place where most naval engineering is focused. They publish a high quality series of technical journals, and deal with real marine engineering, including ships, off-shore platforms, ice-related problems, etc. I joined primarily because they are the only ones who seem to be concerned with a particular vibration problem that interests me. I have not solved that problem yet, but when I do, I'm sure I will publish the results in a SNAME journal.

    For contrast with SNAME, there is the American Society of Naval Engineers. I became aware of this organization when I worked for the US Navy, and found that it is mostly Navy officers, government big-shots, government contractors, and others, all pretending to be engineers. Their meetings (I went to several) are about as technical as a comic book. The only reason to be a member here is for the contacts one might make; the technical content is just about nil.

    So, back to the main question: Is it worth it?
    That depend entirely on your own goals and values. Are you interested in it for a social outlet? Are you interested in terms of community service? Are you hoping it may provide you a contact that could lead to a better job? Are you hoping to learn serious new engineering content? Before I would commit to one of these organization, I would try to investigate just how it fits into your own hopes.
    Most such organizations welcome visitors to your meetings, so you can probably visit a time or two and get some feel for the organization at your local level. Ask what does it do? What projects has it undertaken? Ask yourself if the meeting is well run and organized (I'd stay clear of disorganized groups; they are simply too boring for words!) Ask how often they meet, and what they do in their meetings. I have been on some really excellent field trips as part of various society meetings, and I have often taken students with me to these meeting where there was a field trip involved. I have also been to some really terrible meetings, with a dinner of rubberized chicken and a meandering, dull-as-dust speaker. They vary all over the map.
    I would suggest that every engineer should probably be a part of some such organization, but that should be chosen with real care. Check out prospects very carefully, find out what you might expect to get out of it, what you might expect to contribute, and what the financial cost is. Their can be real benefits, but not every possible choice leads to them. Make a wise choice!
    DrD is a retired Professor of Mechanical Engineering in the USA. He can be reached for comments, questions, or requests through the ME Forum message system.. Be sure to check back soon at www. for more articles.


Professional Responsibility — Do The Right Thing

In Western culture, three professions are recognized. They are medicine, the law, and theology. The practitioners of these professions have long been accorded a special status in society in recognition of their special knowledge. The physician is expected to use his knowledge of healing only for good, and never to murder or maim a person. The lawyer is expected to give correct legal advice to his clients, to keep them free from legal entanglements. The theologian is expected to always correctly guide folk in the right way according to their faith, so that they avoid eternal condemnation. In every one of these professional roles, the professional person is seen as a protector of society at large.

Engineering has much more humble beginnings. In the earliest days, engineers were simply builders of whatever was needed, whether it be a canal, a windmill, a bridge, or a fortification. As such, they were carpenters, stone masons, blacksmiths, etc. Over time, with the application of mathematics, engineering has gradually become recognized as a profession, similar to the classical professions. It is based on a core of specialized knowledge, and it has a responsibility to society at large to protect that society. Thus the man who designs and constructs a bridge assumes responsibility for assuring that the bridge will not fall. The man who designs a complex assembly machine assumes a responsibility that (1) the machine will function and not be a waste of the investor’s money, and (2) that the machine will function safely and not endanger the workers nearby.

Everyone recognizes that professional people are still just people, and thus prone to failure. Doctors sometimes perform surgeries that kill the patient. Lawyers sometimes give unsound advice and their clients suffer as a result. Engineers occasionally design systems that do not function as expected, but in every case, the intent of the professional person must be the protection of the individual client first and also of society at large.

Many readers of ME Forum are either engineering students or new graduates. As you enter into the role of an engineer, you are acquiring a respected status, and you are also taking on professional responsibilities. You have a duty to assure that society is well served, that people are not endangered, either in their physical safety or their finances. This does not mean that you cannot participate in high risk ventures. But it does mean that it is your duty to be sure everyone is fully informed of the risks involved. An example of this is the US moon landing program. This was certainly a high risk program, and there were a few failures along the way. The good part, from a professional perspective, is that everyone was kept fully informed of the risks, so that no one was mislead.

One of the areas where there is much misinformation today is energy sources. This is a “hot area,” in the sense that there is much excitement about “new energy sources.” Solar power, wind power, wave power, in-situ coal combustion, and so forth, are all ideas being explored as people look for cheaper and non-polluting energy sources. All of these are really not new; they have been exploited to a very limited degree for many years. They are “new” only in the sense that there is an expanded interest in them, particularly driven by current economics.

At the beginning of this article, I discussed the characteristics of a profession, both in terms of status of the practitioners and their responsibilities to society. There is another class of people who also claim to possess special knowledge, the Con Man. These are magicians, astrologers, soothsayers, witch doctors, etc. They gain the confidence of their clients by trickery, and deliberately mislead them to the advantage of the con man. (The term Con Man refers to someone who operates by first gaining the confidence of his victim.)

In the 19th century American west, the "snake oil salesman" was a commonly encountered con man. He typically traveled from town to town, peddling his patent medicines which he claimed could cure everything from gout, cancer, tuberculosis, appendicitis, liver failure, blindness, deafness, and failed love affairs. While no such medication has ever existed, this did not stop those suffering these various aliments from seeking his products. They wanted to believe him because of their suffering. The term “snake oil,” implying an oil extracted from some breed of snake, was commonly used to describe these phony medications that were usually nothing more than alcoholic drinks in medicine bottles.

The critical thing about the snake oil salesman is that his customers wanted to believe what he was telling them. They wanted relief from their ailments, and thus they believed the most absurd claims. We have a similar situation today in terms of the energy area. There are all sorts of con men operating, promoting schemes that cannot possibly work but that will make them rich if they can be sold to the public. This is where the engineer’s responsibility comes into the picture.

The energy con men often speak in terms of perpetual motion machines, “over unity” magnetic systems (over unity means with efficiencies greater than 100%), and other similar imaginary concepts. I say “imaginary” in that, while we can imagine them and desire them, the laws of physic preclude their existence. In particular, the Second Law of Thermodynamics and the concept of Entropy make such devices impossible. But impossibility has never stopped the con man!

When such confidence schemes are promoted to the public, engineers have a professional responsibility to speak out. We have studied, we have acquired the specialized knowledge required to evaluate such schemes, and we have a duty to protect the public from such con men who only seek to profit from the ignorance of the general public. We have two such confidence schemes in operation here at ME Forums, even though there has been, to the best of my knowledge, no attempt to profit monetarily from these tricks.

The first is presented in an article titled “Gravitation - Energy of the Future,” begun by a poster called Sentally, on 8 October, 2015 (     not clickable, but copy and paste will work). If you read his article and the comments that follow, you will see a demonstration of the classic confidence operation. He presents his false information, and when challenged, he simply claims superior knowledge that enables him to dismiss his critics without any real explanation at all.

The second is VEProject1's Blog, ( )  On this blog, the author has presented a number of interesting devices that appear to contradict known scientific principles. Some of these are described as perpetual motion machines, other simply as curiosities. The title stands for “Visual Education Project,” but if he was interested in true education, he would explain how his devices work.

You may ask how the systems show on the VEProject blog can be denied when they appear to work in video demonstrations. The answer is simply that the video does not show everything that is involved. There is more to these systems than meets the eye in the video. In a previous post at Mechanics Corner, I examined one of these systems in detail, based upon what is visible in the video. I showed there that the system cannot possibly move under gravity because the center of mass is stationary (The VEProject --- Shifted Levers --- A Critical Assessment).

So, how do these devices work? I cannot say for certain, but there are several possibilities:
1. Perhaps the most obvious is computer graphic trickery, where the video has been manipulated to show something that never really happened.
2. Perhaps there is a hidden motor, driving the system through concealed belts and/or gears. This would have to be done with considerable skill, but it is certainly possible.
3. One of the most interesting possibilities is that of manipulation of powerful magnets below the table.

This last is interesting from a technological standpoint. Permanent magnets have been known to man for a very long time, but really powerful permanent magnets are a relatively recent improvement. This has been brought about the application of various rare earth elements such as Samarium-Cobalt. Today, using rare earths, we have permanent magnets far more powerful than the permanent magnets of previous generations, and many people have looked in this direction for a “new” energy source. I think such a search is misguided, but I cannot say that it is impossible. But if it is necessary to move the permanent magnets, that movement constitutes a work input to the system, and must be taken properly into account.

So, where does professional responsibility come into the ME Forum discussion? As engineers, we have the duty, the obligation, to call out false demonstrations wherever they are shown. If we fail to do this, we are tacitly endorsing the false representations. We do not want to be put in the position of having someone invest in ignorance in such schemes, thinking that we approve of them. We have a responsibility to speak out against falsehood wherever it is found.

For this reason, I urge every reader of ME Forums to review the material presented by these two frauds and then to protest to the site owner by an internal e-mail (saurabhjain Administrator). These sites should be urged first to make a correct, honest presentation of their ideas. If that is not done, they should be removed from ME Forums. It is time for all Forum readers to speak up! We have to do the right thing!


As most of us know, the Internet is a fantastic resource for information. You can find information on almost any topic you can imagine by doing an Internet search on the appropriate keywords. The flip side of this capability is that you can also find mis-information on almost any topic because there is no one to monitor the Internet for correctness. Wikipedia is a classic case in point. Many of the Wikipedia articles are highly informative and very valuable. Some, however, are highly biased and incorrect.

We have such a problem here on the ME Forum with a blog titled Differences Between SI Engine and CI Engine by ibrahim1hj. This blog author has posted a large tabular comparison of these two engine types in the About section of the blog, a place where there is no ability for anyone to add a comment. This would not be a problem except that there is a serious need to comment on this information; some of it is misleading at best. I am reproducing below the table in question, and will comment on it below the table:

From ibrahim1hj ---

About this blog

Spark Ignition (SI) engine can be compared with Compression Ignition (CI) engine system in 7 aspects. Those 7 aspects are engine speed, cycle efficiency, fuel used, time of knocking, cycle operation, pressure generated and constant parameter during cycle.




Spark Ignition Engine


Compression Ignition Engine




Engine speed


SI engines are high speed engines.


CI engines are low speed engines.




Cycle efficiency


SI engines have low thermal efficiency


CI engines have high thermal efficiency.





Fuel used


Petrol is used as fuel, which has high self ignition temperature.


Diesel is used as fuel, it has low self ignition temperature.




Time of knocking


Knocking takes place at the end of combustion.


Knocking takes place at the beginning of combustion.




Cycle operation


SI engine works on otto cycle.


CI engine works on diesel cycle.




Pressure generated


Homogeneous mixture of fuel, hence high pressure is generated.


Heterogeneous mixture of fuel, hence low pressure is generated.




Constant parameter during cycle


Constant volume cycle.


Constant pressure cycle.


DrD again here.

In his first comparison item, he says that "SI engines are high speed engines," but that "CI engines are low speed engines." Well, what does that mean? What is "high speed" and what is "low speed"? Who defines these terms? (ibrahim1hj certainly does not provide a definition.) We are left to wonder what this tells us.

Actual engine speed ranges all over the place, so terms like "high" and "low" do not mean much without providing context. Many years ago, when I was actively involved in the engine industry, I worked for a company that sold many thousands of diesel engines that had a nominal speed in the range 1800 to 2000 rpm. These were 2 stroke diesels. We also sold some much larger engines (again, 2 stroke diesels) that ran at 900 rpm, which I thought of as being "slow." More recently, I have done some work with large marine diesels that run at 90 to 110 rpm. On the other hand, this past weekend, I was at an antique engine show where I saw a number of spark ignited engines that ran at 100 to 300 rpm. My SI automobile engine easily turns up around 5000 to 6000 rpm and will go higher. My truck has an SI engine that does not like to run much over 3000 rpm top speed.

Therefore the original statements in terms of "high speed" and "low speed" are just about meaningless. I have given examples of both SI and CI engines that run at speeds all over the place. I suggest that the meaningless terms "high speed" and "low speed" should not be used in an article on ME Forum, but rather give specific values if at all possible.

Regarding comparison items 6 and 7, "Pressure Generated" and "Constant Parameter during Cycle" there are some additional difficulties. Ibrahaim1hj says that, for an SI engine "high pressure is generated" but for a CI engine "low pressure is generated." While ibrahim1hj does not specify, we might reasonably presume that he is referring to peak cylinder pressure. He goes on to describe the Otto cycle (SI engine) as employing constant volume while the Diesel cycle (CI engine) is a constant pressure cycle. The cycle descriptions are correct as far as they go, but they contribute to the idea that the diesel engine cylinder pressures are lower than those for the SI engine; this is not correct.

Actual firing cylinder pressure data is hard to obtain, but there is some information available in a very old reference (F.P. Porter, "Harmonic Coefficients of Engine Torque Curves," J of Applied Mechanics, Trans ASME, March, 1943). In this paper, Porter gives P-V diagrams and torque-piston position diagrams for a wide variety of engines. Set B2 shows a maximum cylinder pressure of about 760 psi for a 4 stroke gasoline engine (this would be an SI engine). He shows several different data sets (G1, H1, J2) for two stroke diesel engines with maximum cylinder pressures of 670, 840, and 1150 psi. For a four stroke diesel engine, he shows data sets (P2 and Q2) with maximum firing pressures of 740 and 930 psi. In most cases, the maximum firing pressures for the diesel engines exceed that for the gasoline engines. Thus it would appear that the comparisons given by ibrahim1hj are exactly backwards.

It is important to be able to check the validity of what we read on the Internet, and to verify the sources. One thing that helps in this regard is the ability to comment on items posted. Comments can both expand on the information given, and can also offer correction to errors in articles. We need this capability.


ODE Solution --- Fail!!


Mechanics Corner
    A Journal of Applied Mechanics and Mathematics by DrD, # 31
      Machinery Dynamics Research, 2016

ODE Solution --- Fail!!



    Digital computation has become a major tool for engineers, and it is a great benefit. It can also lead to many pitfalls for the unwary. This note is about the latter, a potential pitfall that many engineers risk on a daily basis, most of them with little awareness of the danger.
    Early in the development of digital computation, every problem required that the user write a program specific to the problem at hand. If speed was a very important issue, the programs were written in machine language, so that they would execute as fast as possible. If speed was a little less critical, programs were written in so-called "high level languages." This included FORTRAN, BASIC, ALGOL, C, C++, and a host of other such names. But even with a high level language, there was the problem of generating a program for the solution of the specific problem at hand.
    As things have continued to evolve, it was soon evident that a lot of the work in writing each program was the same from one problem to the next. The major mathematical operations, such things as numerical integration, matrix operations and the solution of systems of linear equations, plotting, and many other steps were re-usable from one problem to the next. It was natural that this would eventually lead to the development of general purpose programs, able to solve broad classes of problems. This group includes programs like Mathematica, Maple, MatLab, SciLab, Maxima, TKSolver, and numerous others. Most of those just mentioned have built-in capability to solve ordinary differential equations, in some cases by analytical means, and in practically all cases, by numerical means. This has taken the sting out of working with differential equations
from many engineering problems, and we must all be grateful for that.
    At the same time, we must also be somewhat skeptical about any general purpose solver when applied to a particular problem. How do we know that the solution generated is correct? How do we even know if it is reasonable? Most of the time, when engineers resort to numerical solutions, it is because there is no readily available analytical solution. Thus, when faced with a problem that cannot be solved in closed form, how can we know when to trust the numerical solution? This is a very serious question, one that all must consider. It you blindly trust a numerical solution, the old excuse, "The computer said it was OK" will not get you very far. The computer cannot be fined, fired, or (in extreme cases) possibly sent to prison, but all of these things can happen to an engineer!
    So, what can the engineer do when the differential equation has no known solution? Well, there are several options.
    (1) He can resort to any physical principles that apply to the situation. For example, if the system is such that energy should be conserved, then he can add code to calculate the total system energy at every instant. Just verifying that energy is conserved does not "prove" that the solution is correct, but if energy is not conserved when it should be, you can be sure there is an error in the solution.
    (2) He can try various approximations that may apply to see if they are in reasonable agreement with the computed solution.
    (3) He can verify the solution code by applying it to a similar problem for which there is a known solution. It is this last approach that I want to talk about in this post.



Modeling Hysteresis

Mechanics Corner

A Journal of Applied Mechanics and Mathematics by DrD, #41

(c) Machinery Dynamics Research, July 2017


Modeling Hysteresis

1. Introduction

What do you know about hysteresis? Many Mechanical Engineers will associate this term with the magnetization curve of a piece of magnetic material, and quickly conclude, "I don't have to worry about that!" But that would be wrong. While hysteresis does occur in magnetic systems, it happens in many other situations as well, many of them situations of concern to mechanical engineers.


Figure 1 Typical Hysteresis Curve


Figure 1 shows a typical hysteresis curve, and it makes no difference as to what physical phenomena are involved. The red curve is the actual hysteresis curve. The blue curve is called the "spine."


41 Modeling Hysteresis.pdf