Sunday, May 6, 2012

Comparing Gigawatt Electric Plants with Hiroshima

By definition, it is hard to comprehend other orders of magnitude--their very label "order of magnitude" points to their otherness and separateness. But the news is full of information from other orders of magnitude. To serve their readers, journalists and other authors recruit metaphors to explain this information from foreign scales.

A staff writer in the Economist's special report on nuclear reactors used such metaphors to explain the power of gigawatt reactors:

The energy output of that first reactor was tiny: just half a watt. Today’s most powerful reactors produce ten billion times as much energy in the form of heat, about a third of which can be converted into electricity. Five gigawatts is an amount beyond easy comprehension, the daily equivalent of the energy given off by six bombs like the one that destroyed Hiroshima. 

The math seems wrong to me, here. A 5 GW plant in a day yields 4.32 x 10^14 Joules. According to the Manhattan Project memorial site, the Little Boy Hiroshima bomb yielded 15 kilotons of explosive energy, or 6.276 x 10^16 Joules. So a 5 GW plant, in a day, releases the energy of 2/3rds of a Hiroshima bomb.

The Hiroshima Bomb has become a defacto unit of measurement for comparisons like this. Unfortunately, the scale is radically different. The bomb completed its energy release in under a second, while a power plant works for billions of seconds; the bomb radiated energy in all directions while powerplant energy is measured only as per the useful energy generated in a wire, and so on.

The author then uses similar metaphors to describe the rapid historical growth of nuclear technology.  
If flights had lasted a billion times longer 70 years after the Wright brothers’ first one took off, they would have gone a thousand times round the world and taken centuries; a billion times faster, and they would have run up against the speed of light. Even at the heady rates of progress that Moore’s law ascribes to the computer industry (stating that the number of transistors on a chip doubles roughly every two years), things take 60 years to get a billion times better.
This is an innovative comparison, and works due to the nature of "a billion." People are often surprised that a billion seconds takes over 31 years to elapse. Again, the change in scale is poorly understood.

NOTE: This post starts a new series of posting metaphors, with our commentary or critique. If you read an interesting metaphor that stands out either for its clarity or confusion, send it to me, scalometer at gmail dot com.

Links and References

The Economist article:
Manhattan Project website:


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