Math and Science
Engineering Design and Problem Solving
Engineering is that profession in which the energy, forces and materials of nature are made useful to mankind. The engineer is known for his ideas that employ natural science, mathematics, computer analysis, art and his overall experiences in order to produce or improve a product or service useful to humans or to enrich their lives.
High school students almost never contact engineering in their classes since they experience only those courses representing the working tools necessary for the engineer, primarily mathematics, science, and computers. A student's interest in one ore more of these areas might lead to his becoming an excellent and useful engineer.
The mathematician uses the exact laws of mathematics to arrive at mathematical conclusions that may or may not pertain to actual situations within the world. As a rule, he does not concern himself greatly with what his mathematical quantities represent or mean, leaving these for others to interpret in terms of real things in the world.
The scientist describes the behavior of the universe in written laws he can understand, then uses them to predict the possibility of specified occurrences in the real world and related information descriptive of these occurrences.
The computer scientist concerns himself with the internal operations of a computer system which best can perform mathematical and decision making processes useful to the mathematician, scientist, engineer, business man and others in a manner requiring the least computer time with the greatest possible related accuracy.
The artist creatively produces a painting, object, composition, or structure that is appealing to the aesthetic sense of the general public. Generally he has no need to consider the structural soundness of his created object.
The engineer employs the fundamentals of mathematics, science, computer science, art and expertise gained through his/her experiences to analyze his creative ideas in various manners in order to arrive at optimal decisions concerning his recommendations in a manner beneficial to mankind. Because of this, the manner in which an engineer approaches a design or problem usually differs appreciably from the approaches common to scientists, mathematicians, and others.
The Six Major Steps in the Engineering Approach to Designs or Problems are as follows:
Recognition of the need: Realization of the need to make a change in something, or the desirability of accomplishing something for which currently no successful or good solution exists, such as the need for a cleaner air or for improved utilization of parking areas. The recognition of this need and stating this need in words understood by others often is a creative process done by engineers, but sometimes by others as well.
Definition of the problem: Usually states in general what should be accomplished, without providing a listing of possible methods of accomplishing the desired result, such as removal of noxious material from the atmosphere. The definition of the problem specifies what is desired to be accomplished, including pertinent system parameters currently existing or desired, such as creation of twenty parking spaces in the existing lot marked off for fifteen spaces.
Synthesis: This is the most creative activity of the engineer, and consists of suggesting new ways of looking at the existing problems, new ways of applying known procedures to new conditions, or alternate possible designs which might meet the specifications of the problem. This creative activity usually is enhanced by the expertise of the engineer gained through experience. The probability of an individualÕs having a creative idea increases with the summation of total creative ideas he has had during his entire life.
Analysis and optimization: Consists of evaluation of the several different possible creative design ideas, picking the one(s) which seem best to meet the problem specifications, and optimizing the parameters of these "best" designs, selection of the one "best overall" design, and optimization of the parameters which best meet the overall desirable features required by the problem definition, including preventing those items from occurring as required by the problem statement, such as preventing collapse of aircraft landing gear upon landing of the airplane.
Evaluation of the optimized design: Consists of an overall evaluation of how well this design meets the desired requirements of the problem definition in addition to how well it restricts from occurring those items forbidden by the problem statement.
Presentation of the optimized design: Consists of the engineer's communicating his final design to others, particularly to those who will manufacture the designed product, to distribute it, and to sell it. This is done by freehand sketches with appropriate notes and dimensions, scaled assembly and detail drawings with parts list and associated worded specifications, by models of the designed prototype, by word communication (both oral and written), or by a combination of these methods.
Recognition of the need to do something and expressing this need in words is a creative process not unique to engineers. Usually it is based upon one's experience in life rather than upon his technical competence in mathematics, science, or the use of computers. The aesthetic need to improve the overall appearance of something is enhanced by oneÕs experiences in artistic areas.
Definition of the problem frequently result from one's experience in living; however, use of physical scientific information is also helpful.
Synthesis of possible designs is almost entirely at the mercy of the creative capability of the individual concerned, usually very little enhanced by technical competence.
Analysis and optimization of the design employs mathematics, science, and often the use of computers in order to result in the best overall design.
Evaluation of the optimized design is something engineers acquire through experience; however, mathematics, science and computers often are useful in providing the designer with information necessary in order for him to be able to make this evaluation correctly.
Presentation of the optimized design is a communication skill acquired through experience in relaying information from one individual to another. For an engineer, by those proficient in production methods, or by those managers responsible for making decisions relating to which products shall be put onto the market, whether a specific product will be improved, and related items. Usually mathematics, science and computers are of little use to the engineer in presenting his final design.
In the six phases of engineering design, excluding the presentation of final design phase, backtracking or iterating to an earlier stage frequently is necessary or desirable, such when as the analysis and optimization of the various design possibilities indicate the criteria stated in the problem definition can be met well, and that new synthesized designs creatively must be determined, or possibly even iterating back to the problem definition to redefine the problem in a manner that the desired results can be accomplished to satisfy the original need for the design. Whenever the status of one's design process indicates the backtracking to an earlier stage in the design is desirable or necessary, as one progresses forward again in his design, he may be able to skip one or more intermediate stages that require no modifications in its results.
Excluding the analysis and optimization stage and the evaluation of the design state, college courses usually do not provide much if any occasion for students to recognize the need, to define the problem, to synthesize possible alternate designs, or to present his final optimized design. The senior engineering design projects are notable exceptions to this statement.
The following suggestions are made in order to improve the student's overall capabilities in analysis, optimization, and evaluation of engineering designs:
Thoroughly read (and reread if necessary) the entire problem statement prior to making any attempt to solving the problem. State the problem in your own words, referring back to the original problem statement if necessary in order to be able to complete your own statement of the problem. The most important item is to state clearly and as briefly as feasible, what is known, what is to be determined, and any additional items which are to be determined. Sometimes explaining to others your understanding of the problem statement until they understand it assists you in clearly formulating you own statement of the problem.
Upon occasion too much or too little information is given in the initial statement of the problem. Disregard unnecessary information. State the need for additional information, probably using considered judgment to assume the missing information (which later on in the design hopefully can be verified as being valid).
Draw a sketch, block diagram, or free body diagram of the situation, including important variables and other necessary information. Be sure to indicate coordinates if such are a part of your solution.
Consider alternate possible methods of solving the problem: What information is required in order to be able to use each method, and what degree of accuracy of results does each method provide?
In order to come up with creative design alternatives, brainstorming sessions conducted by a group of three to perhaps twelve individuals usually yield a far greater number of creative possibilities than the aggregate suggestions of the same total number of individuals working independently of each other. During such sessions, it is important that merely the possible design alternative be listed without any attempt to evaluate at all any of the alternatives. This can come later on during the analysis and optimization phase of design.
Select what appears to be the best overall method of solution in order to achieve the desired results.
Use the "best" procedure to obtain results as required by the problem statement.
Evaluate your result for practicality, producibility, and acceptability by the public. Economic considerations of production and distribution also are important considerations.
After you finally have obtained suitable and acceptable results meeting the requirements of the problem, present your results in a manner understood clearly by others. This can be done sometimes by use of a simple statement, by underlining your answers or putting them in a block and giving units and directions if applicable, in tabular form, by use of curves, or in any other manner which best might describe your results in a manner understood by others proficient in the area of study represented by the problem.
Remember that sometimes there is no "correct or acceptable answer," and sometimes there may be several "correct" answers, depending upon assumptions made and the creative design selected. Particularly in cases where the problem is "overstated" it may be impossible to meet all criteria required by the problem statement. In such cases, state the existing conditions and make whatever recommendations seem best to meet as many criteria as possible, stating which criteria are not met and how much they fail to be satisfied.