The Various Principles of Approximations in Design Engineering

Real structures and circuits are usually too complicated to compute exactly. Modern computers with programs such as finite element analysis have made enormous breakthroughs in computing the performance of physical systems. However, even they require some simplifying assumptions, and they are time-consuming to apply to the early design of a new product. Therefore it is useful for design engineers to develop skill in approximation and simplifying assumptions. Then, as the design converges to its final form, either pencil and paper or computer analysis, or both, can be used for more exact performance and sizing calculations.

Insight

The most basic requirement for approximating with minimum error is an insight into the behavior of the product and its components. This is a glittering generality which is easy for me to say but impossible for me to explain. Nevertheless, it is true, and you should consciously try to imagine the spread of stress and strain, the flow of currents and generation of voltages, and the motion of material in your mental image of the product. Just as you make and improve a mathematical model inside a computer, you should make and continually improve an imagination model inside your head.



Seven Principles of Approximation

1. One of the techniques of approximation is the substitution of lumped parameters for distributed parameters. For example, in a structure loaded with spread loads you can substitute concentrated loads at what you judge to be appropriate positions. In electrical devices it is common to make such approximations; for example, the distributed leakage inductance and capacitance of a transformer winding is almost perfectly represented by a lumped inductance in series and a lumped capacitance in parallel with a leakage-free winding. (In the case of high-frequency transients such as lightning strokes on a power transformer this approximation breaks down.)
   
   
2. You can approximate the device itself by omitting details and by replacing complex portions with approximately equivalent simple portions.
   
   
3. Your approximation does not even have to conform to the laws of nature. For example, Prof. Herbert C. Roters of the Stevens Institute of Technology developed a technique of computing the reluctance of a magnetic field by approximating the shape of the field with a set of geometric shapes each having an average length and average width and adding the parallel reluctances of the shapes. For the approximation to be "true" there would be points of infinite flux density, yet the calculations match experimental measurements with surprising accuracy.
   
   
4. The roughest approximation is used in testing the practicality of the earliest conception of the product. Then, as the design is developed and refined, the degree of approximation is reduced.
   
   
5. There are advanced CAD programs which will do almost exact analysis of structures and devices as they are sketched into the terminal. If you have and can use such a computer and software, then you need do little approximation.
   
   
6. The undesirability of exact definitions and categories in the early-thinking phase of your work. The use of such undefined words is a qualitative approximation.

This article is not an appeal for inaccuracy; it is an approach to efficiency so that you can reach maximum useful accuracy with the least time and work.