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Engineering calculations on a PC

Original article date: January 1999

Every time you see a technical document where parts of a formula have been added in by hand because the word processor used can’t handle mathematical symbols, you’re reminded that the folks behind PC-based maths software have still got plenty of potential users to go for.

There are several applications on the market which will turn your PC into a tool which can solve those equations and print them out too – and do a lot more besides. Two came our way towards the end of last year, but as we know exactly what this sort of software can do, we thought it would be more interesting to give them to a reader who hadn’t been exposed to the suppliers’ marketing machines. Arthur Redsell takes a look at the latest versions of two of the longest established PC-based maths toolkits on the market…

From logs to models

Over the last forty years we have replaced our log tables and slide rules by electronic calculators, extended the scope of the calculators to include all sorts of in-built trigonometric and statistical functions and then widened the applications to handle whole fields of data in the form of numerical ‘spreadsheets’ on our computers. Within the spreadsheets, the many available ‘functions’ help us perform repetitive mathematical operations quickly of whole fields of data – and if need be, to plot out the results.

Essentially, spreadsheets are intended to deal with multiple manipulations of relatively simple complexity, although the degree of manipulation which the formulas can achieve will also depend on the mathematical knowledge and skill of the operator as well as the range of in-built functions available.

Now, over in industrial design, once the intuitive and artistic ideas have been formed, there is a need to prove the integrity and reliability of the concept through the application of mathematical analysis. Here ever more complex formulas and functions come into the design calculations along with the necessity to solve the equations which themselves model the functioning of any proposed system. While the ‘flair’ may be fun, the proof is often hard-bitten graft, and not what our spreadsheets offer us. Enter the two maths programs which we have been looking at this month: TK Solver Release 3 and Mathcad 8.

Both of these are complex, expensive, specialist programs which are unlikely to interest the happy dabbler. Just as the fanciest, spell-checking, grammar-correcting, word processor is never going to turn its user into a Shakespeare or a Wordsworth, so similarly neither TK Solver 3 nor Mathcad 8 is going to turn a novice into a mathematician. Users will need to have a very good grounding in maths to be able to use these programs successfully. But in competent hands the software will be of enormous benefit to designers in handling the calculations which they must do to satisfy themselves that their ideas are practical and reliable.

TK stands for ‘Tool Kit’ and the TK Library provides an extensive selection of files under the categories of Utilities, Mathematics, Statistics and Applications along with numerous examples of their use. These built-in demonstrations can, at further cost, be supplemented by whole libraries of examples taken from such standard works as Roark and Young’s treatise on stress calculations, and from standard ‘works’ on thermodynamics, finance, machine design, queuing theory and etc.

Mathcad 8 goes to similar lengths to provide the beginner with adequate guidance on how to set up a problem for solution. It is this procedural technique which the novice is going to have to master and it is where the user’s learning curve will be the steepest. The manner of doing this differs between the two programmes.

TK requires the problem which requires a solution to be set out on a ‘Rule Sheet’ with a build-up somewhat akin to creating a Spreadsheet. The rules define the relationships between the variables and other quantities, with the variables then automatically appearing on another ‘Variable Sheet’ on which Input or Output Values can be set. Other sheets define lists of values, functions, unit conversions etc. In the ‘Mathlook’ sheet a snapshot of the equations is built up.

The Mathcad 8 approach is different, but equally widespread in application, and appealed somewhat more to me personally because here the problem was defined exactly as it would have been if worked by hand on the blackboard or workbook, the resulting layout looking just like a text book example.

In addition to the numerous example workings, both programs are backed up by extensive files of functions and tables of properties. The functions available cover Integral and Differential Calculus, Boolean Logic, Matrices and Iterative calculations with the ability to produce 2D and 3D plots of the data.

Wizards are on hand to help with setting up and all the usual facilities to drag and drop, link and embed to produce first rate reports including as much or as little detail (or hidden propriety data) as is required or is commercially desired.

World Wide Web interchange of ideas and new solutions, plus the usual technical back-up facilities, make these powerful programs a very worthwhile investment for those people involved in the design of products and systems where mathematical analysis is at the heart of their job. Come to think of it, where is it not? AR

January 1999

Added on 18 February 2009 at 4:33 pm | Read more cad articles