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Application of Trigonometry in Engineering


Trigonometry is the part of mathematical subject which deal with the length of the sides of right triangles and based on similar triangle relationship. The fundamental concept or idea of trigonometry is extended beyond right angle triangles. Study of trigonometry goes in depth of  basic calculus. They deal certain rotation of an angle  called as a trigonometric function. Graphing calculating technology is used to enhance the grade level of students .The calculator provides a  quick graph for both simple and complicated equations involving trigonometric function. A large collection of examples of all the functional problems are provided with each exercise in the  book.


Trigonometry identities are implemented in architectural design to find the length of the side of constructing a building, identifying the physical models,etc,Trigonometry is used in all application fields like astrophysics,chemistry,physics,geography,architecture,study of waves, frequency,etc. By making use of trigonometric function the magnitudes of wave and frequency distribution are calculated and plotted on the graph with respect to time.

Application of Trigonometry in Engineering:

A wide range of piratical trigonometric application is found in engineering by making use of trigonometric function like sine, cosine, tangent, secant, cosecant and cotangent. The theorems like sine and cosine rule, Pythagorean theorem are used mostly. The engineering subject like mechanical, civil, aerospace,dynamics, etc it deals with the application of trigonometry to do research like to calculate the velocity of an object,the distance between celestial bodies in space, construction of buildings, the rate of water drains fro the field,wind correction in space for flights, line of sight.

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From Wikipedia

Value engineering

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 “Each 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 system’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 “value analysis�.

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:

  1. Preparation
  2. Information
  3. Analysis
  4. Creation
  5. Evaluation
  6. Development
  7. Presentation
  8. Follow-up

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.

Gather information

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?

7.Present ideas

Sell alternatives

Chemical engineering

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:


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 (1763–75) 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

Aircraft engine

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