Spherical Livestock

Doug Bell

If, like me, you are a fan of the sitcom The Big Bang Theory, you may have heard the Spherical Chicken joke in the episode “The Cooper-Hofstadter Polarization:”

There's this farmer, and he has these chickens, but they won't lay any eggs. So, he calls a physicist to help. The physicist then does some calculations, and he says, “I have a solution, but it only works with spherical chickens in a vacuum.”

When I saw the episode with my family, I laughed out loud at the joke (probably a little too much like the nerdy characters) and received strange, but not unfamiliar, looks from my wife and sons. The joke has existed for years starring a veritable barnyard of orb-like livestock such as a poorly performing race horse and low-yield dairy cattle. The punchline is always the same, though: the problem is solved with improbable assumptions.

Engineers (and physicists) understand the joke. We often apply simplifying assumptions to make a problem manageable. These assumptions take many forms: incompressible fluids, inviscid flow, lumped capacitance, to name a few. The very equations used by analysis software are based on simplifying assumptions.

While the trend has been for engineers to include details in the analysis software and let it mesh and run, there is much to be gained by using simplifying assumptions. I am not saying that detailed models don't have their place, but simplified models have their place and are often overlooked.

A simple model provides insight into the key physics of the problem. By stripping out all but the most basic physics and adding them back in one at a time, you understand what affects the solution. Also, your solution does not waste time on irrelevant physics that may require unnecessarily complicated calculations. For example, if you need to find out if albedo from the Moon and Earth are both significant during a transfer orbit, model a sphere (it can be a chicken or a horse) and have it traverse away from the Earth and toward the Moon without worrying about the geometry or trajectory. A quick review will determine if both reflected solar loads are worth including in the system model at all times.

A simple model makes validation easier. A simple model can make it easier to perform the necessary calculations by hand to ensure the model does not have errors before moving toward more complex calculations. I had a supervisor who would not allow anyone to present a thermal analysis without first presenting a sketch of the system's energy balance. A simple model allows evaluating each input and output.

A simple model solves quickly. A fast-solving model allows evaluating more design options while a detailed model will be more constrained. Investigating a wider possibility of designs can lead to an unexpected design. The ability to run many cases quickly also enables correlating the model to test data. This provides further validation of the model and strengthens the trust in the model when it is used to evaluate untestable conditions. Statistical treatment of uncertainties provides another reason for having a fast-running model.

A related note: you can always present the results of a simple model along with the assumptions, but you cannot present the results of a complex model if it is not complete.

So, while the spherical animals make for a good punchline, they have their place in analysis. Just be sure you don't stop at the simplest model so you don't become the joke.