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:

- Relevance: Connect the primary motivations/needs/objectives for the experiment (performance, efficiency, foutputs, etc.) to the key variables for the experiment (resistances, potentials, inputs, etc.).
- Efficiency: Establish only enough of the theory 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 quantify 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. Now, before we spent considerable funds on equipment and instruments, we had a very good reason to do the experiment and knew what we needed to measure. So, how do we go about actually doing our theory/analysis?

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, StarSolve, etc).
- Take whatever units you have and immediately convert everything to base SI (m,s,kg,Pa,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.
- Determine key performance metrics for your experiment. Remember how most performance metrics are determined:

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

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. Once validated, these curves save substantial money and time.

Being able to quantitatively show where the losses that caused the actual to be worse than the ideal tells 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