Originally posted Apr 2, 2016
This one really is rocket science
For engineers, intuition is uniquely powerful, but not infallible. It can come from physical analogies, mathematics, similar previous experiences, pattern recognition, the implications of fundamental natural laws, and many other sources.
I have a lot of respect for intuitive analysis and conclusions, but I’m especially interested in situations where it fails us, and especially in understanding why it failed. Because I like to avoid erroneous conclusions, I often find that understanding the specific error points to a better intuitive approach.
Previously, I wrote about one intuitive assumption and its flaws, and also about a case in which a simple intuitive approach was perfectly accurate. This time, I’d like to discuss another example related to power and energy, albeit one that has very little to do with RF measurements.
Let me set the stage with this diagram of an interplanetary spacecraft, making a close pass to a planet as a way to steal kinetic energy and use that boost to get where it’s going faster.
An interplanetary spacecraft is directed to pass near a planet, using the planet’s gravity field to change the spacecraft trajectory and accelerate it in the desired direction. Equivalent rocket burns at time intervals a and b produce different changes in the spacecraft’s speed and kinetic energy. (Mars photo courtesy of NASA)
One of the most powerful tools in the engineer’s kit is the law of conservation of energy. RF engineers may not use it as often as mechanical engineers or rocket scientists, but it’s an inherent part of many of our calculations. For reasons that escape me now, I was thinking about how we get spacecraft to other planets using a combination of rockets and gravity assist maneuvers, and I encountered a statement that initially played havoc with my concept of the conservation of energy.
Because most rocket engines burn with a constant thrust and have a fixed amount of fuel, I intuitively assumed that it wouldn’t matter when, in the gravity-assist sequence, the spacecraft burned its fuel. Thrust over time produces a fixed delta-V and that should be it… right?
Nobody has repealed the law of conservation of energy, but I was misapplying it. One clue is the simple equation for work or energy, which is force multiplied by distance. When a spacecraft is traveling faster—say finishing its descent into a planet’s gravity well before climbing back out—it will travel farther during the fixed-duration burn. Force multiplied by an increased distance produces an increase in kinetic energy and a higher spacecraft speed.*
My intuition protested: “How could this be? The math is unassailable, but the consequences don’t make sense. Where did the extra energy come from?”
One answer that satisfied, at least partially, is that burning at time b rather than time a in the diagram above gives the planet the chance to accelerate the spacecraft’s fuel before it’s burned off. The spacecraft has more kinetic energy at the start of the burn than it would have otherwise.
Another answer is that the law of conservation of energy applies to systems, and I had defined the system too narrowly. The planet, its gravity field, and its own kinetic energy must all be considered.
Fortunately, intuition is as much about opportunity for extra insight as it is about the perils of misunderstanding. Lots of RF innovations have come directly from better, deeper intuitive approaches. In the wireless world, CDMA and this discussion of MIMO illustrate intuition-driven opportunities pretty well. Refining and validating your own intuition can’t help but make you a better engineer.