Machine Design

Math software pushes the parametrics

Probably one of the best features in the mathematical-engineering program Mathcad Version 14.0 is that it works directly with Pro/Engineer.

Greg O'Neill


The equations in Mathcad (bottom) describe the electric field for a portion of a four-filament helical antenna. The plot shows the summed patterns from each filament (0 through 20).

This lets engineers use the math software to parameterize Pro/E drawings using formulas ranging from simple functions to sophisticated sets of equations.

Despite its capability, the software is easy to use. As with past versions, users enter calculations in something like a word processor. The software then performs calculations and displays results. Areas called Text Regions provide handy spaces for typing in descriptive text that documents engineering reasoning. Mathcad also lets users build reports, proposals, and technical papers — even whole textbooks.

The software supports many different levels of mathematics. For example, it calculates explicit (represented by numerical quantities) as well as symbolic (represented by equations) results. Of course, the program solves single equations with one unknown, but it also handles large systems of linear, nonlinear, and differential equations with multiple unknowns. V 14 also lets users see underlying calculations. This is in contrast to application-specific software, which often does not let users see how calculations are performed.

Mathcad's good graphic capabilities help users tell a story in words and numbers. Results are graphed as 2D or 3D plots using lines or surfaces to illustrate mathematical functions. In addition, the software includes a feature for setting up range variables that form the basis of graphs. This comes in handy when performing iterative calculations. Such graphs make it easy to see tolerance issues after establishing the fundamental mathematical relation.

The program helps ensure that calculations are correct by checking for dimensional consistency. And it provides format placeholders that help users enter equations. New users will appreciate the tutorials, quicksheets, and Getting Started primers. In addition, reference tables in the software list commonly needed data for engineering calculations. These improvements often have me urging engineers and students who have used Mathcad in the past to give the software a second look.

For document control, Version 14.0 provides formatting aids that let users generate reports that comply with company templates. And the program has improved the way worksheets insert into other documents. Users can save documents as HTML files for viewing in a Web browser, in RTF mode for Word, or as PDF files for Adobe Acrobat.

To better understand improvements to the software, take a look at a recent replotting of a radiation pattern for a quadrifiliar helical antenna I first plotted years ago. The necessary mathematics came from a published paper. I set up the complex integral vector equations and summed the patterns from each filar. Results were plotted as polar graphs. The earlier attempt took many minutes to solve. Today, the software calculated the radiation pattern in a few seconds.

The software comes from PTC Corp., 140 Kendrick St., Needham, MA 02494, (781) 370-5000,

Greg O'Neill is senior RF engineer at SkyCross Inc., Melbourne, Fla., (312) 308-6640, ( SkyCross designs and builds antennas for cellular and wireless devices.

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