In just about every job I’ve been in, people were tempted to label me as either a “theorist” or an “experimentalist”. — Don’t take the bait. It’s easy to fit into a stereotype, tough to break free of them. The very best engineers are competent with both the theory and the experiment. It’s what we call a positive synergy — knowledge of one aids the other.

This brings us to three general guiding principles for the Theory chapter of our reports:

- Relevancy: Connect the primary motivations/needs/objectives for the experiment (performance, efficiency, outputs, etc.) to the key variables for the experiment (resistances, potentials, inputs, etc.).
- Efficiency: Establish only enough of the theory and associated assumptions such that the calculations can be repeated by a fellow engineer without the need to contact you.
- Credibility: At the end of your project, your theoretical predictions should agree with your experimental measurements and you should have justifications for limits to and deviations from theory. Engineers have value because we can predict the future with quantifiable confidence — 95% of the results fall with ±X of the predicted value.

Related to the first principle, when constructing experiments from scratch it is important to determine your key variables a priori (in advance) of building the experiment. This allows you to focus your time and money on the key variables that matter to the client/customer goal. We don’t have the time or money for open-ended fishing expeditions.

Example: My Ph.D. dissertation was on the modeling of visco-plastic flow of solid hydrogenic fuel within twin-screw extruders for the fueling of fusion energy tokomaks. Nobody had built a machine to solidify and extrude solid hydrogen before. Only the most very basic material properties of hydrogen were available! How do we most efficiently build an experiment that helps us develop theory to model how such a machine will operate? Here’s a visual of my first research poster on this subject:

By building a simple numerical heat exchanger model of the vortex tube and varying the key input parameters/variables, we discovered that the two-phase heat transfer, latent heat, and viscous dissipation were the most sensitive operating parameters. The latent heat was known and the two-phase heat transfer coefficient was not necessarily controllable, so the most important parameter for us to know very well in the model was the viscous dissipation, which we could control through heater input. So we built an experiment to measure viscous dissipation very well, and along the way measured the 2-Phase heat transfer coefficient, among other things.

We had a motivated client with a need, searched the literature to know that the need was a gap in the literature/knowledge, and completed a careful calculation to show that an experiment will help solve the need. We now had a very good reason to do the experiment and knew what we needed to measure prior to conducting an experiment.

This isn’t new for you. Each of you learned the scientific method in high school and the concept of a testable hypothesis: “My hypothesis is that if we vary X then we will see a change in Y.” Think ‘if this then that.’ A hypothesis should be testable and falsifiable by yourself or independently by someone somewhere else. Hypotheses were typically generated at the start of a project in high school. I think this is why the scientific method is generally failing so many people. You don’t know enough to develop a relevant, credible, and efficient hypothesis until you’ve got motivation, done a literature review, and made a connection between inputs and outputs with theory. Now’s the time to generate that hypothesis if you need one.

So, how do we go about actually doing our theory/analysis chapter for our reports?

Here’s a few modeling steps:

- If you are still using a calculator, stop. Calculators are typewriters. Use some form of engineering equation processor (EES, Matlab, Excel, Python, etc). Program the most basic equations that connect the input variables to the output measurements.
- Take whatever units you have and immediately convert everything to base SI (m, s, kg, Pa, V, etc.). Base SI is the only self-consistent unit system. Read my post – End US Engineering Education of English units for more. It’s a huge loss to our national economy that gets worse every year. You will solve your problems faster, with fewer mistakes in base SI. EES will easily convert and check your units are consistent for you. Convert your final plots into whatever units your clients can best handle.
- Conduct an Uncertainty/Sensitivity analysis of your programmed equations. This is possible by simply varying each of the inputs by 10% and watching how much each variation effects the desired output. EES can numerically conduct this type of sensitivity analyses with one click.
- Determine key performance metrics for your experiment. Remember how most performance metrics are determined:

1st Law System Performance = (What you want)/(What you paid to get it)

2nd Law Device/Component Performance = (What you got)/(What you could’ve) a.k.a. (actual)/(ideal)

With these programmed, you can now make performance/design curves on plots that can help you to determine where to take measurements. Nobody in 406 has every began an experiment linearly varying input variables only to discover the output to be highly non-linear. Save yourself the time and check the theory in advance. Once validated, these performance curves save substantial money and time.

Being able to quantitatively show where the losses that caused the actual to be worse than the ideal shows you know how best to improve the system and gives you value as an engineer. Once completed, the report will naturally transition to the need to actually do the experiment to test the theory.

In the end, at the minimum, you need to show with math how the inputs are connected to the outputs via variables, and know which variables are most important over what ranges.

“No matter how bright you are or clever your theory is, if it doesn’t agree with experiment, it’s wrong.” ~Richard Feynman

“Through measuring is knowing.” ~Heiki Kammerlingh-Onnes