Pi = 3!
Here, you can use pi
In one of my high school math classes I remember the teacher telling us about some of the American states that, apparently feeling uncomfortable with digits to the right of the decimal point, tried to legislate that pi should be exactly equal to 3. The teacher scoffed and, being dutiful math students, so did we. And when I brought the story home, my mom scoffed as well (she was a science teacher – my dad, a history and English teacher, took a few moments to realize that he should also scoff at this). So imagine my surprise when, not many years later, I found myself in Naval Nuclear Power School, learning how to calculate the radiation dose from an extended source – a contaminated wall, for example – and our instructor told us “And here, you can use pi … but for our purposes pi equals 3.”
ZUSAMMENFASSUNG
Mit der Aussage Pi = 3 wird angedeutet, dass in vielen Routinefällen eine grobe Abschätzung der Strahlung ausreichend ist, um sinnvoll reagieren zu können. Mit Beispielen wird gezeigt, dass hier Zeitersparnis Leben retten kann. So wird praktischer Strahlenschutz der gesellschaftlichen Herausforderung gerecht.
SUMMARY
Pi = 3
The statement Pi = 3 shows that in many routine cases a rough estimate of the radiation is sufficient to be able to react appropriately. Examples are used to show that saving time can save lives. This is how practical radiation protection meets the social challenge.
Calculations didn’t need to be more precise than the instruments
“And here, you can use pi…but for our purposes pi equals 3”
I knew better than to scoff – my Boot Camp pushups were not very far in the past – but my hand shot up, along with several of my classmates. The instructor didn’t call on anyone; he gave a small smile and said “I know, I know. But before you get too outraged, try to remember that your radiacs can be off by as much as 20% and still pass calibration.” Our hands went down, albeit a bit more slowly than they’d been raised.
From this, I developed a general rule of thumb that, for any work that involved making measurements, my calculations didn’t need to be more precise than the instruments I’d be checking them with. Over the years it’s saved me a tremendous amount of time and worry, it’s saved my various employers and consulting clients a fair amount of time and money as well. And all without arousing the ire of my regulators!
Rules of thumb to make it easier
Something else I’ve spent a lot of time on is rules of thumb to make it easier to make a quick guess as to whether or not I should be concerned about a situation.
As one example, I can look up the gamma constant for 137Cs – 2.26 x 10-17 Gy s-1/(Bq/m2) – or, in units I’m more likely to use, about 0.301 R hr-1/ (Ci/m2).
For a rough guess, I can just divide my source’s activity (in Ci, mCi, or µCi) by 3 for a conservative estimate of dose rate a meter away in R/hr (sorry – as with pints, miles, and Fahrenheit, I think best in my native units). I’ve got other quick-and-dirty estimates for other common radionuclides, for the decay of fallout from nuclear weapons explosions, for radiation exposure to the fetus from x-rays, CT, and fluoroscopy, and more.
Purpose of quick estimates
The purpose of these quick estimates is not to come up with a number that I can publish in the peer-reviewed literature – the purpose is to quickly figure out if there’s something I need to worry about enough to do a more careful and formal calculation.
For example, if I got a call late at night about a woman brought in unconscious after a traffic accident who was given the normal head-to-foot “trauma series” of x-rays and, when she woke up, told her doctor she was pregnant I felt comfortable telling the emergency room doctor that a few x-rays were unable to produce enough fetal dose to cause concerns; if the doctor said that they’d done an abdominal CT as well I was comfortable that the dose was low enough to still be safe; if they’d also had to do fluoroscopy then I knew the dose might be high enough to warrant a bit of calculation at the moment and a more complete calculation when I got to work in the morning.
Using these quick estimates didn’t necessarily replace formal calculations so much as to let me know if I could do them when time permitted or if I needed to do them right away.
What do I need to know about this?
When I started working for the police and the fire department – and especially when we did some exercises together – I realized that quick estimates were even more important. This was driven home by a cop during a training exercise – we were involved in a training exercise in which (simulated) terrorists were trying to steal a high-activity radioactive source from a blood-bank irradiator.
“OK, Doc – what do I need to know about this?”
“Well – it’s a 2500-Ci source of 60Co… the gamma constant is a little more than 1.1 R/hr per curie at one meter …”
And he cut me off. “Doc – I don’t need to know any of that – I’ve got one guy who wants to blow me up and another one who wants to shoot me. Just tell me where to stand and how long I can stay there.”
And I realized that I didn’t need to convince him that I was doing the calculations correctly or how I was doing them – all he cared about…the only thing that was important to him … was quickly being able to say “You’re OK over there for ten minutes or so.”
Bottom line
The bottom line is that there are times we need to be precise … and there are times that “good enough” is good enough for what we need to accomplish. If we’re responding to an emergency, striving for meaningless accuracy or precision can cost lives, although such situations are, admittedly, nothing that we’re likely to experience frequently.
But even in more routine circumstances, we need to realize that there are times– there are a lot of times – where we really don’t need to spend the time hammering out an answer with a few more significant digits – when what we really need is simply an answer that moves us in the right direction.