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Mathcad® is the right solution for the job at Dynamic Air

Len Williams, Managing Director of Dynamic Air in the UK, is finding Mathcad a better answer to many in-house problems that he would once have had to write dedicated programs to solve. With Mathcad, it is easy to re-use calculations in other projects or share routines with colleagues, so there is no unnecessary reiteration of work already done.

Dynamic Air, Inc. has, in just over 30 years since its formation, established itself as a worldwide force in bulk materials movement. From bases in Australia, Brazil, the US and the UK, Dynamic Air’s pipelines serve customers and licensees across five continents. Ten thousand of their industrial-scale systems move substances ranging from ABS resin to zirconium silicate, in huge quantity, for industries as diverse as steel production, pharmaceuticals and wastewater management. These systems are, as the corporate name implies, pneumatic; the aim is to maintain smooth fluid-like flow of finely divided product or raw material at high speed through the stages of a given mass process.

The systems are built to four basic models, from a portfolio listing some thirty or so fundamental types of component, but all share a common dependence on pipelines built from a limited range of modular sections. Finding and communicating the most efficient combination of these sections is one area where Mathcad has helped save both time and resources, without the need for programming from scratch.

Changes of direction in a pipe are constructed from two root bends (B/6 and B/12 radians respectively). Judicious multiple combination of these segments, in conjunction with suitable rotation about the local pipeline axis at the points of junction, can yield any three-dimensional change in direction. The tricky part is achieving the best solution; time is money, and solving such bends unaided is a time-consuming business that Mathcad was well equipped to streamline.

A few minutes spent playing with models reveals that beneath apparent simplicity lies a visualisation and manipulation problem on a par with Rubik’s cube. Real world pipelines also encounter complicating factors such as space and route constraints, plane displacement of the pipeline as well as a change in direction, and a need to solve anew at every bend. Len Williams tackled the problem with a Mathcad-based “ready reckoner” aid, which turns input problems into output answers more quickly, transparently and easily than the manual or programmed alternatives.

“The solution was an exercise in matrix manipulation,” explains Len. “The initial three dimensional bases needed to be set up, the matrices of transition calculated and then used to operate on the various bases and the vectors which represent the segments. Finally, we needed to determine the angle that we needed to twist the first segment on the incoming pipe to bring the direction of the outgoing pipe into a plane parallel to the plane it would have occupied if we had not twisted the segments relative to each other.”

Sound confusing? It is, until you get Mathcad involved. Although Len modestly describes himself as “not at all proficient,” the worksheet he created is efficient and well documented, literally talking the user through solutions involving up to ten segments. This is greatly aided by the text-page nature of Mathcad, encouraging natural language approaches that facilitate speed and clarity. An opening table of values is followed progressively by matrix layouts, local bases and vectors, as Mathad’s flexible mix of text and symbolics clearly steps the user through full explanations of what the sheet is doing, and why, as intermediate and final values are computed.

Looking to the future, Len says that he would like to add diagrams or other visual illustrations, again using Mathcad’s facilities or the bundled SmartSketch application, to further amplify and clarify the process for unfamiliar users. Len’s whole worksheet is a textbook example of the advantages of Mathcad’s open, word processor approach over traditional spreadsheet or language-programmed approaches, especially when it comes to the speedy development and communication of human-friendly mathematical solutions.

Mathcad 11 is supplied and supported in the UK, Ireland, Denmark and Norway by Adept Scientific plc, Amor Way, Letchworth, Herts. SG6 1ZA; telephone (01462) 480055, fax (01462) 480213, email mathcad@adeptscience.co.uk; or see Adept’s World Wide Web site http://www.adeptscience.co.uk/. Adept Scientific is one of the world’s leading suppliers of software and hardware products for research, scientific, engineering and technical applications on desktop computers.

With offices in the UK, USA, Germany and throughout the Nordic region, Adept Scientific is one of the world’s leading suppliers of software and hardware products for research, scientific, engineering and technical applications on desktop computers.