Application of Trigonometry in Engineering
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Value engineering (VE) is a systematic method to improve the "value" of goods or products and services by using an examination of function. Value, as defined, is the ratio of function to cost. Value can therefore be increased by either improving the function or reducing the cost. It is a primary tenet of value engineering that basic functions be preserved and not be reduced as a consequence of pursuing value improvements.
In the United States, value engineering is specifically spelled out in Public Law 104-106, which states â€œEach executive agency shall establish and maintain cost-effective value engineering procedures and processes."
Value engineering is sometimes taught within the project management or industrial engineering body of knowledge as a technique in which the value of a systemâ€™s outputs is optimized by crafting a mix of performance (function) and costs. In most cases this practice identifies and removes unnecessary expenditures, thereby increasing the value for the manufacturer and/or their customers.
VE follows a structured thought process that is based exclusively on "function", i.e. what something "does" not what it is. For example a screw driver that is being used to stir a can of paint has a "function" of mixing the contents of a paint can and not the original connotation of securing a screw into a screw-hole. In value engineering "functions" are always described in a two word abridgment consisting of an active verb and measurable noun (what is being done - the verb - and what it is being done to - the noun) and to do so in the most non-prescriptive way possible. In the screw driver and can of paint example, the most basic function would be "blend liquid" which is less prescriptive than "stir paint" which can be seen to limit the action (by stirring) and to limit the application (only considers paint.) This is the basis of what value engineering refers to as "function analysis".
Value engineering uses rational logic (a unique "how" - "why" questioning technique) and the analysis of function to identify relationships that increase value. It is considered a quantitative method similar to the scientific method, which focuses on hypothesis-conclusion approaches to test relationships, and operations research, which uses model building to identify predictive relationships.
Value engineering is also referred to as "value management" or "value methodology" (VM), and "value analysis" (VA). VE is above all a structured problem solving process based on function analysis—understanding something with such clarity that it can be described in two words, the active verb and measurable noun abridgement. For example, the function of a pencil is to "make marks". This then facilitates considering what else can make marks. From a spray can, lipstick, a diamond on glass to a stick in the sand, one can then clearly decide upon which alternative solution is most appropriate.
The Origins of Value Engineering
Value engineering began at General Electric Co. during World War II. Because of the war, there were shortages of skilled labour, raw materials, and component parts. Lawrence Miles, Jerry Leftow, and Harry Erlicher at G.E. looked for acceptable substitutes. They noticed that these substitutions often reduced costs, improved the product, or both. What started out as an accident of necessity was turned into a systematic process. They called their technique â€œvalue analysisâ€�.
The Job Plan
Value engineering is often done by systematically following a multi-stage job plan. Larry Miles' original system was a six-step procedure which he called the "value analysis job plan." Others have varied the job plan to fit their constraints. Depending on the application, there may be four, five, six, or more stages. One modern version has the following eight steps:
Four basic steps in the job plan are:
- Information gathering - This asks what the requirements are for the object. Function analysis, an important technique in value engineering, is usually done in this initial stage. It tries to determine what functions or performance characteristics are important. It asks questions like; What does the object do? What must it do? What should it do? What could it do? What must it not do?
- Alternative generation (creation) - In this stage value engineers ask; What are the various alternative ways of meeting requirements? What else will perform the desired function?
- Evaluation - In this stage all the alternatives are assessed by evaluating how well they meet the required functions and how great will the cost savings be.
- Presentation - In the final stage, the best alternative will be chosen and presented to the client for final decision.
How it works
VE follows a structured thought process to evaluate options as follows.
1.What is being done now?
- Who is doing it?
- What could it do?
- What must it not do?
2.How will the alternatives be measured?
- What are the alternate ways of meeting requirements?
- What else can perform the desired function?
3.What must be done?
- What does it cost?
4.What else will do the job?
5.Which Ideas are the best?
6. Develop and expand ideas
- What are the impacts?
- What is the cost?
- What is the performance?
- Sell alternatives
Chemical engineering is the branch of engineering that deals with the application of physical science (e.g., chemistry and physics), and life sciences (e.g., biology, microbiology and biochemistry) with mathematics and economics, to the process of converting raw materials or chemicals into more useful or valuable forms. In addition to producing useful materials, modern chemical engineering is also concerned with pioneering valuable new materials and techniques - such as nanotechnology, fuel cells and biomedical engineering. Chemical engineering largely involves the design, improvement and maintenance of processes involving chemical or biological transformations for large-scale manufacture. Chemical engineers ensure the processes are operated safely, sustainably and economically. Chemical engineers in this branch are usually employed under the title of process engineer. A related term with a wider definition is chemical technology. A person employed in this field is called a chemical engineer.
Chemical engineering timeline
In 1824, French physicist Sadi Carnot, in his "On the Motive Power of Fire", was the first to study the thermodynamics of combustion reactions. In the 1850s, German physicist Rudolf Clausius began to apply the principles developed by Carnot to chemical systems at the atomic to molecular scale. During the years 1873 to 1876 at Yale University, American mathematical physicist Josiah Willard Gibbs, the first to be awarded a Ph.D. in engineering in the U.S., in a series of three papers, developed a mathematical-based, graphical methodology, for the study of chemical systems using the thermodynamics of Clausius. In 1882, German physicist Hermann von Helmholtz, published a founding thermodynamics paper, similar to Gibbs, but with more of an electro-chemical basis, in which he showed that measure of chemical affinity, i.e., the "force" of chemical reactions, is determined by the measure of the free energy of the reaction process. The following timeline shows some of the key steps in the development of the science of chemical engineering:
- 1805â€“ John Dalton published Atomic Weights, allowing chemical equations to be balanced and the basis for chemical engineering mass balances.
- 1882â€“ a course in "Chemical Technology" is offered at University College London
- 1883â€“ Osborne Reynolds defines the dimensionless group for fluid flow, leading to practical scale-up and understanding of flow, heat and mass transfer
- 1885â€“ Henry Edward Armstrong offers a course in "chemical engineering" at Central College (later Imperial College), London.
- 1888â€“ There is a Department of Chemical Engineering at Glasgow and West of Scotland Technical College offering day and evening classes.
- 1888â€“ Lewis M. Norton starts a new curriculum at Massachusetts Institute of Technology (MIT): Course X, Chemical Engineering
- 1889â€“ Rose Polytechnic Institute awards the first bachelor's of science in chemical engineering in the US.
- 1891â€“ MIT awards a bachelor's of science in chemical engineering to William Page Bryant and six other candidates.
- 1892â€“ A bachelor's program in chemical engineering is established at the University of Pennsylvania.
- 1898â€“ Bachelor of science program in chemical engineering is established at the University of Michigan.
- 1901â€“ George E. Davis produces the Handbook of Chemical Engineering
- 1905â€“ the University of Wisconsin awards the first Ph.D. in chemical engineering to Oliver Patterson Watts.
- 1908â€“ the American Institute of Chemical Engineers (AIChE) is founded.
- 1922â€“ the UK Institution of Chemical Engineers (IChemE) is founded.
Chemical engineering is applied in the manufacture of a wide variety of products. The chemical industry has a large scope, manufacturing inorganic and organic industrial chemicals, ceramics, fuels and heat engine that performs mechanical work using steam as its working fluid.
The idea of using boiling water to produce mechanical motion has a long history, going back about 2,000 years. Early devices were not practical power producers, but more advanced designs producing usable power have become a major source of mechanical power over the last 300 years, beginning with applications for removing water from mines using vacuum engines. Subsequent developments using pressurized steam and converting linear to rotational motion enabled the powering of a wide range of manufacturing machinery. This could be sited anywhere that water and coal or wood fuel could be obtained, whereas previous installations were limited to locations where water wheels or windmills could be used. Significantly, this power source would later be applied to prime movers, mobile devices such as steam tractors and railway locomotives. Modern steam turbines generate about 80% of the electric power in the world using a variety of heat sources.
Steam engines are typically external combustion engines, although other external sources of heat such as solar power, nuclear power or geothermal energy may be used. The heat cycle is known as the Rankine cycle.
In general usage, the term 'steam engine' can refer to integrated steam plants such as railway steam locomotives and portable engines, or may refer to the machinery alone, as in the beam engine and stationary steam engine. Specialized devices such as steam hammers and steam pile drivers are dependent on steam supplied from a separate boiler.
The history of the steam engine stretches back as far as the first century AD; the first recorded rudimentary steam engine being the aeolipile described by Greek mathematician Hero of Alexandria. In the following centuries, the few steam-powered 'engines' known about were essentially experimental devices used by inventors to demonstrate the properties of steam. A rudimentary steam turbine device was described by Taqi al-Din in 1551 and by Giovanni Branca in 1629.
Following the invention by Denis Papin of the steam digester in 1679, and a first piston steam engine in 1690, the first practical steam-powered 'engine' was a water pump, developed in 1698 by Thomas Savery. It proved only to have a limited lift height and was prone to boiler explosions, but it still received some use for mines and pumping stations.
The first commercially successful engine did not appear until around 1712. Incorporating technologies discovered by Savery and Denis Papin, the atmospheric engine, invented by Thomas Newcomen, paved the way for the Industrial Revolution. Newcomen's engine was relatively inefficient, and in most cases was only used for pumping water. It worked by using the vacuum from condensing steam in a cylinder and was mainly employed for draining mine workings at depths hitherto impossible, but also for providing a reusable water supply for driving waterwheels at factories sited away from a suitable 'head'.
The next major step occurred when James Watt developed (1763â€“75) an improved version of Newcomen's engine, with a separate condenser. Watt's engine used 75% less coal than Newcomen's, and was hence much cheaper to run. Watt proceeded to develop his engine further, modifying it to provide a rotary motion suitable for driving factory machinery. This enabled factories to be sited away from rivers, and further accelerated the pace of the Industrial Revolution.
Newcomen's and Watt's early engines were "atmospheric", meaning that they were powered by the vacuum generated by condensing steam instead of the pressure of expanding steam. Cylinders had to be large, as the only usable force acting on them was atmospheric pressure. Steam was only used to compensate for the atmosphere allowing the piston to move back to its starting position.
Around 1800, Richard Trevithick introduced engines using high-pressure steam. These were much more powerful than previous engines and could be made small enough for transport applications. Thereafter, technological developments and improvements in manufacturing techniques (partly brought about by the adoption of the steam engine as a power source) resulted in the design of more efficient engines that could be
An aircraft engine is the component of the propulsion system for an aircraft that generates mechanical power. Aircraft engines are almost always either lightweight piston engines or gas turbines. This article is an overview of the basic types of aircraft engines and the design concepts employed in engine development for aircraft.
Engine design considerations
The process of developing an engine is one of compromises. Engineers design specific attributes into engines to achieve specific goals. Aircraft are one of the most demanding applications for an engine, presenting multiple design requirements, many of which conflict with each other. An aircraft engine must be:
- reliable, as losing power in an airplane is a substantially greater problem than in an automobile. Aircraft engines operate at temperature, pressure, and speed extremes, and therefore need to perform reliably and safely under all reasonable conditions.
- light weight, as a heavy engine increases the empty weight of the aircraft and reduces its payload.
- powerful, to overcome the weight and drag of the aircraft.
- small and easily streamlined; large engines with substantial surface area, when installed, create too much drag.
- field repairable, to keep the cost of replacement down. Minor repairs should be relatively inexpensive and possible outside of specialized shops.
- fuel efficient to give the aircraft the range the design requires.
- capable of operating at sufficient altitude for the aircraft
Unlike automobile engines, aircraft engines are often operated at high power settings for extended periods of time. In general, the engine runs at maximum power for a few minutes during taking off, then power is slightly reduced for climb, and then spends the majority of its time at a cruise setting—typically 65 percent to 75 percent of full power. In contrast, an automobile engine might spend 20 percent of its time at 65 percent power while accelerating, followed by 80 percent of its time at 20 percent power while cruising.
The power of an internal combustion reciprocating or turbine aircraft engine is rated in units of power delivered to the propeller (typically horsepower) which is torque multiplied by crankshaft revolutions per minute (RPM). The propeller converts the engine power to thrust horsepower or thp in which the thrust is a function of the blade pitch of the propeller relative to the velocity of the aircraft. Jet engines are rated in terms of thrust, usually the maximum amount achieved during takeoff.
The design of aircraft engines tends to favor reliability over performance. Long engine operation times and high power settings, combined with the requirement for high-reliability means that engines must be constructed to support this type of operation with ease. Aircraft engines tend to use the simplest parts possible and include two sets of anything needed for reliability. Independence of function lessens the likelihood of a single malfunction causing an entire engine to fail. For example, reciprocating engines have two independent magneto ignition systems, and the engine's mechanical engine-driven fuel pump is always backed-up by an electric pump.
Aircraft spend the vast majority of their time travelling at high speed. This allows an aircraft engine to be air cooled, as opposed to requiring a radiator. With the absence of a radiator, aircraft engines can boast lower weight and less complexity. The amount of air flow an engine receives is usually carefully designed according to expected speed and altitude of the aircraft in order to maintain the engine at the optimal temperature.
Aircraft operate at higher altitudes where the air is less dense than at ground level. As engines need oxygen to burn fuel, a forced induction system such as turbocharger or supercharger is especially appropriate for aircraft use. This does bring along the usual drawbacks of additional cost, weight and complexity.
History of aircraft engines
- 1633: Lagari Hasan Ã‡elebi took off with what was described to be a cone shaped rocket and then glided with wings into a successful landing (although this account is considered legend)
- 1848: John Stringfellow made a steam engine capable of powering a model, albeit with negligible payload
- 1903: Karl Jatho He tested his plane on August 18, 1903 and managed to make hops of up to 3 m (10 ft) in height for a distance of 60 m (200 ft).
- 1903: The Wright brothers commissioned Charlie Taylor to build an inline aeroengine (12 horsepower) for the Wright Flyer
- 1906:Traian Vuia flew his first airplane "Vuia I" at Montesson on 18 March. He made a hop of 20 Meters at an altitude of 1 Meter using compressed carbonic acid as a power scource.
- 1908: RenÃ© Lorin patents a design for the ramjet engine
- 1909: Roger Ravaud' GnÃ´me rotary engine in Henry Farman's aircraft won the Grand Prix for the greatest non-stop distance flown - 180 kilometres (110 mi) - and created a world record for endurance flight
- 1910: Henri Coanda an unsuccessful From Encyclopedia
SIC 3724 Aircraft Engines and Engine Parts
This industry includes establishments primarily engaged in manufacturing aircraft engines and engine parts. This industry also includes establishments owned by aircraft engine manufacturers and primarily engaged in research and development on aircraft engines and engine parts, whether from enterprise funds or on a contract or fee basis. Also included are establishments engaged in repairing and rebuilding aircraft engines on a factory basis. Establishments primarily engaged in manufacturing guided missile and space vehicle propulsion units and parts are classified in SIC 3764: Guided Missile and Space Vehicle Propulsion Units and Propulsion Unit Parts; those manufacturing aircraft intake and exhaust valves and pistons are classified in SIC 3592: Carburetors, Pistons, Piston Rings, and Valves; and those manufacturing aircraft internal combustion engine filters are classified in SIC 3714: Motor Vehicle Parts and Accessories. Establishments primarily engaged in the repair of aircraft engines, except on a factory basis, are classified in SIC 4581: Airports, Flying Fields, and Airport Terminal Services; and research and development on aircraft engines on a contract or fee basis by establishments not owned by aircraft engine manufacturers are classified in SIC 8731: Commercial Physical and Biological Research. 336412 (Aircraft Engine and Engine Parts Manufacturing) The total value of complete aircraft engines was approximately $6.4 billion in 2002, according to the U.S. Census Bureau. This amount represented a decrease from 2001 levels of $7.3 billion and 2000 levels of $7 billion. In addition to decreasing shipment values, unit shipments also declined during the early 2000s. Although figures were not available for 2002, units fell from 15,626 units in 2000 to 13,571 units in 2001. The consumption of aircraft engines is obviously a function of aircraft production and usually a multiple function due to the fact that many aircraft have several engines. The health of the aircraft industry is well documented under SIC 3721. However, during the early 2000s the larger aircraft industry was feeling the negative effects of a downturn in the air transportation sector. This downturn affected orders for new aircraft and thus had an impact on the market for aircraft engines. Although the U.S. Census Bureau recorded nine firms within the industry in December 2002, the world aircraft engine industry is dominated by three companies: General Electric (GE); Pratt & Whitney, which is a division of United Technologies Corporation; and Rolls-Royce. Each of these companies achieved its leading role through the successful development of jet engine models for commercial aircraft, though GE and Pratt & Whitney maintained significant interest in the development of engines for military aircraft. The big three offered jet engines in nearly every thrust range and competed with each other for use on commercial aircraft produced by Boeing and Airbus S.A.S. Several other engine manufacturers, including Textron, Inc.'s Lycoming, were involved primarily with small jet turbines and piston engines, which power propeller-driven aircraft. Aircraft engine manufacturers enjoyed a long period of industry growth from the end of World War II until the first years of the 1990s, when changes in military spending and changing commercial air travel patterns caused dramatic shifts in industry planning and expectations. By the late 1990s, the future of the aircraft engine market seemed likely to depend on the development of big engines with a thrust of 60,000 pounds or more, according to Interavia. Each of the leading engine manufacturers was expected to develop engines in this category. By late 2002 GE offered its GE90 turbofan engine, capable of generating 115,000 pounds of thrust. The manufacture of aircraft engines was once controlled by the same companies assembling aircraft and operating airlines, but industry regulation initiated in 1934 forced aircraft engine manufacturers to work independently of aircraft manufacturers. This antitrust legislation is partly responsible for the intense competition that characterizes the aircraft engine industry in which each of the leading engine makers seeks to provide engines to fit the requirements of a wide range of aircraft. Engine companies are typically chosen to design an engine at the concept stage of a new aircraft. Once the engine is developed, the engine builder may try to adapt the design for other aircraft. In fact, it is common to find the same engine on a variety of competing aircraft. Engine manufacturers rarely develop an engine that is not capable of multiple applications. For decades following the end of World War II, military funding supplied much of the research and development money that allowed U.S. manufacturers to continually upgrade their engines. Technical breakthroughs achieved on military projects found their way into commercial engine applications, thus allowing engine manufacturers to achieve substantial profits from commercial engine sales. This arrangement changed significantly after the end of the cold war when the U.S. military budget decreased dramatically. Thus, engine manufacturers were increasingly faced with incorporating the cost of research and development spending into the price of their engines. The leading American aircraft engine manufacturers are divisions of larger corporations. For example, Pratt & Whitney is a division of United Technologies, GE Aircraft Engines is a unit of General Electric, and Lycoming is part of Textron. Pratt & Whitney and GE are thought to possess an advantage over their British competitor, Rolls-Royce, because of their corporate support, which allows them to better withstand industry cycles. The development of powered aviation, which began with the Wright Brothers in 1903, fell mainly to those who understood engines, rather than those who understood flight. In fact, aeronautical scientistsâ€”such as Samuel P. Langley, who was perhaps the first to describe the dynamics of lift over a wingâ€”had very little to do with powered aircraft. Instead, a pair of bicycle mechanics, Wilbur and Orville Wright, and a motorcycle mechanic named Glenn Curtiss, were the first to demonstrate propeller-driven aircraft. In fact, Curtiss gained an early lead over the Wrights and a third aviator, Glenn Martin, precisely because he knew how to build lighter, more powerful motors. The first 10 years of motorized flight was pioneered by eccentric inventors working out of their garages by night and flying in air shows by day. These barnstormers relied on show earnings to pay for their building efforts, and many died in the process. Industrial support for aviation did not materialize until European aviators demonstrated the strategic use of aircraft in World War I. Major industrial involvement in the United States occurred only after the U.S. Army requested funding for aviation projects. Financiers and industrial magnates were drawn to the industry not by their love of aviation, but by the opportunity to enrich themselves with government contracts. Some of the earliest investors in aircraft ventures were automobile manufacturers and automobile fleet owners. They sponsored specific aircraft builders and later pulled dishonest financial stunts to take control of aircraft builders' fledgling companies. Edward Deeds, founder of Delco and the first to commercialize an electric starter, formed a one-sided partnership with the well-known Orville Wright called the Dayton-Wright Company. The company built engines, but no aircraft. The company was later acquired by William Boyce Thompson, who established the first American aircraft combine. Thompson acquired the patents owned by Wright and later Martin; he bought the rights to a light, European-designed engine called the Hispano-Suiza, and he acquired the facilities of the Simplex Automobile Company in which to build his engines. Shut out from the management of the company by Thompson and unhappy at only building engines, Wright retired and Martin started another company. Unwilling to allow any single group of financiers to corner the aviation industry, U.S. gover
From Yahoo AnswersQuestion:Trigonometry, Algebra, & Geometry Details: You are a high school math teacher and are introducing matrices to the classroom next week. It is very important to you to make a connection between the real world and this topic, so you decide to research in which applications matrices are used. To your surprise, you find several very useful applications, such as decoding and encoding messages, and decide to discuss two that you feel are important to the class. In the first paragraph, describe the two applications you chose (do not use decoding and encoding) and how they relate to matrices. Then in another paragraph, describe how you would present your lesson to the class.
Answers:Use any IB diploma book on Mathematics. Interdisciplinary relations is one important thing in IB mathematics.Question:The advantage of a fuel cell over conventional batteries is the fuel cell does not require Method of Production of Energy Match the method of production listed above with the object below. (Use each number only once.) A.Hydroelectric plant B.CANDU reactor C.Coal-burning electric plant D.Sun 1. Fusion 2. Fission 3. Free Fall 4. Combustion Compare and contrast thermal power stations with hydroelectric power stations in terms of energy conversions. A heat engine is a device that converts 1.chemical energy into thermal energy. 2.thermal energy into chemical energy. 3.thermal energy into mechanical energy. 4.mechanical energy into thermal energy. In a cold substance, atoms or molecules vibrate[BLANK]than in a hot object. What is the difference between a heat engine and a heat pump? Give a technological example of each. The gunpowder engine was designed by
Answers:1. see wikipedia 2. This really isn't hard at all. Sun=fusion burning=combustion 3. see wikipedia 4. unlike humans in cold 5. see wikipedia 6. see http://library.thinkquest.org/C006011/english/sites/huygens.php3?v=2Question:Hello. I am totally stumped on this question. It is an algebraic story problem in which it pretty much gives you the answer, sort of, and then you have to figure out how to represent the equation, then solve for x. Here it is: In testing an engine, various mixtures of gasoline and methanol are being tried. How much of a 90% gasoline mixture and a 75% gasoline mixture are needed for 1,200 L of an 85% gasoline mixture? I'm just not sure how to begin this question. If anyone knows what I'm talking about, please don't hesitate to help me! Thx!
Answers:////////// x be amount of 90% 0.9x+0.75(1200-x)=1200*0.85 x=800L of 90% 400L of 75%
From YoutubeTrigonometry :SkyingBlogger.Com - for more videos on Trigonometry.This is the first video of trigonometry. This is an introduction videos of Trigonometry. In this trigonometric video we discuss the fundamental concepts of trigonometry, why we study trigonometry in maths, where we apply trigonometry in maths and other subjects or fields. I mean uses of trigonometry. Then we study the fundamental concepts or fundamental 6 trigonometric ratios which are Sine, Cosine, Tan, Sec, Co sec, & Cot. these trigonometric ratios have vast use in mathematics and engineering. I have talked about some tricks to remember trigonometric ratios that is - Luther has some books of personality & Some People have Curly Brown Hair Those Performed Best. These all the trick in trigonometry we use and where and how we use please watch this introductory video of trigonometry. You understand what is trigonometry after watching the video, I hope so.Introduction to Right Angle Trigonometry Applications :This is an illustration of two right angle trigonometry applications problems.