Modeling

Goals

1. Describe modeling.
2. Excel at modeling

Model

A model is a simplified version of reality, typically created for doing something useful. Examples:

• A map
  
• An architect’s sketch of a proposed building
  
• An estimate of monthly expenses
  
• A math model that predicts the height that a rocket will fly
  
• A scale model airplane built for wind tunnel testing
  
• A role-play scenario used in business training to simulate negotiations
  
• A weather forecast model predicting tomorrow’s temperature and rainfall
  
• A biological model organism (like fruit flies) used to study genetics

Modeling in Engineering

Modeling is the process of creating a model, checking that it is accurate enough for its purpose, and then using it.

Engineering relies heavily on modeling because real systems are usually too complex to solve exactly. Instead of seeking perfect answers, engineers create simplified models that provide approximate answers — answers that are “good enough” to guide design, prediction, and decision-making.

Modeling in Statics

In Statics, modeling is everywhere — but the key is learning how the models in the textbook connect to the real world.

When we study a particle, we are not saying that the real object is literally a point with no size. Instead, we are choosing to ignore its size and shape because, for the problem at hand, they don’t matter.
- Example: A car driving down a straight highway can be modeled as a particle if all we care about is its overall motion.

When we study a rigid body, we are not claiming that real objects never bend or deform. We are assuming that the deformations are so small compared to the overall motion that we can safely ignore them.
- Example: A steel beam in a bridge is not perfectly rigid, but if it only bends a tiny amount, modeling it as a rigid body is accurate enough to predict how loads are carried.

We also model loads in simplified ways:
- A push or pull at a single point → a force
- A twisting action → a moment
- A spread-out effect → a distributed load

The power of Statics is that these simple models let us make sense of very complex systems. Once you see the connection between the models in the textbook and the objects around you — cars, beams, bolts, bridges, even your own knee — Statics becomes much more intuitive and useful.

Mapping: (Real World) ⇔ (Conceptual World)

Mapping is the process of moving back and forth between the real world and the conceptual world. It is like speaking two languages and being able to translate fluently between them.

• Real → Conceptual: We simplify reality into a model we can analyze.
  
• Conceptual → Real: We interpret the results of our model to understand or predict what happens in the real world.

Example: In the real world we see a Boeing 787 flying at 750 kph. In the conceptual world, we might model it as a particle with all the forces adding up to zero.

The skill to develop in Statics is fluency in mapping — seeing real-world situations and quickly knowing what conceptual model to use, then taking conceptual results and applying them back to real objects.

I’ll be emphasizing this through the entire Statics BookCourse.