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  1. 2 points
    DrD

    Rocket Homework Problem

    Mechanics Corner A Journal of Applied Mechanics and Mathematics by DrD, #38 Machinery Dynamics Research, 2017 Rocket Homework Problem Introduction 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. RocketHWProblem.pdf 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.
  2. 1 point
    DrD

    ODE Solution --- Fail!!

    Mechanics Corner A Journal of Applied Mechanics and Mathematics by DrD, # 31 Machinery Dynamics Research, 2016 ODE Solution --- Fail!! Introduction 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. ODE_Soln_Fail.pdf
  3. 1 point
    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. DrD
  4. 1 point
    What is the principle of mechanical refrigeration ? You can answer this question. You can like the best answer. You can share the question You can get updates of new questions on Facebook linkedin twitter & google plus
  5. 1 point
    A right hand helical gear is being cut on a milling machine. What changes in machine setting have to be made to cut a left hand helical gear of same pitch and number of teeth ? You can answer this question. You can like the best answer. You can share the question You can get updates of new questions on Facebook linkedin twitter & google plus