# CHAPTER 12

*MATHEMATICAL MODELING IN DESIGN*

*Math and physics are very much part of the design process!*

**MATHEMATICAL MODELS** are central to design because we have to be able to *predict* the behavior of the devices or systems that we are designing. Every new airplane or building, for example, represents a model-based prediction that the plane will fly or the building will stand without producing unintended, often tragic, consequences. It is important for us to ask: How do we create mathematical models? How do we validate such models? How do we use them? And, are there any limits on their use?

We can't possibly introduce here all of the models and techniques needed to model all the kinds of designs that engineers do. However, we can illustrate some major points and “habits of thought” by analyzing some very basic mechanical and electrical devices. In particular, after discussing some fundamental mathematical modeling ideas, we will model a basic circuit found in electrically powered toy cars and then analyze and design a ladder rung.

## 12.1 SOME MATHEMATICAL HABITS OF THOUGHT FOR DESIGN MODELING

If a client wants a device that has reduced energy consumption as an objective (or a limit on energy consumption as a constraint), we need to have a model of our design to address our client's concerns. Similarly, if we know that users of a ladder will be unsettled by a deflection of a rung ...