The Science of Science Ficton: Estimation

poison-waterWhen writing science fiction, sometimes you have to have some science in there.
The science can come from many places, but one skill that is useful in applying it is estimation1: taking observations and extrapolating them. Sometimes this is to answer specific questions, other times it might be to define the parameters of the story.

A Note On Units

When doing these kinds of estimations, using metric units helps. A lot. I am happy enough to convert metric units into US or British Imperial units for presentation2, but the equalities built into the metric system make these calculations much simpler.

  • 1 litre = 1,000 millilitres
  • 1 mililitre = 1 cm3
  • 1 mililitre of water weighs 1 gram3

I also recommend using exponential notation since that makes comparing and cancelling orders of magnitude much quicker.

Finding An Answer

This is some research I was doing for A New Dawn: how much poison do you need to poison a reservoir?

Some context which might help to explain my search history – the bad guys in A New Dawn are prosecuting a terror campaign against the good people of Portland4. Portland gets its water from snow melt collected in a system of reservoirs called Bull Run.

If you were wanting to scare people, how much nastiness would you have to put in the water?

Wikipedia tells me that Bull Run has been measured to hold between 4×107 and 6×107 m3 of water5. For the purposes of easy calculation, I round that out to 5×107 m3. There are 1,000 litres in a cubic metre, so that’s 5×1010 litres.

Now, what’s a good poison? We’re looking to scare people here rather than kill them, so let’s pick something non-lethal, and of course water-soluble. For no particular reason, I settled on LSD.

One of the amazing things about LSD is how potent it is: the threshold dose is 20-40 µg – that’s micrograms – and a normal dose is in the 100-500 µg range. Again, for the sake of ease of calculation, we’ll aim for a dose of 100 µg.

Let’s say that in order to get the dose into the people they will drink 100ml of water, which is two fifths of a US cup. So, in our reservoir of 5×1010 litres there are 5×1011 drinks.

Therefore, we need:

100µg = 100×10-6 g = 1×10-4 g for each drink, which is 1×10-4 * 5×1011 = 5×107 g of LSD

Let’s say that the LSD we are talking about is a fluid of similar density to water, so that the weight we talk about can be translated into volume directly. This is a highly dubious assumption, but it’ll get us close enough.

5×107 g = 5×107 ml = 5×104 litres

For the sake of argument, let’s say we pack the LSD in 55 gallon drums. Now it so happens that 55 gallons is about 200 litres, so you would need:

5×104 / 200 = 2.5×102 = 250 x 55 gal drums

… which is rather less than I expected, in fact, although it’s still a lot: right around 50 tons.

Back to Reality

Is this a credible threat for a reservoir the size of Bull Run?

No – or at least not in our world. Moving that weight would take five ten ton trucks, and the forest roads are not built for that kind of vehicle. The bad guys in A New Dawn of course have other resources which I will not go into here, but even so 250 barrels is a lot.

I toned things down for the game, in the end, loading up a boat with 75 drums instead, since I figured that would still deliver a threshold dose, especially if the victims drank more than half a cup of water.

[1] the sine qua none of estimation is Randall Munroe’s What If? site. There’s a useful discussion of Fermi estimation there too, which would be valuable for capturing the basic plausibility of a notion.

[2] I won’t talk about the differences between those two systems, except to note that the US label “standard units” is gratuitously wrong.

[3] at Standard Temperature and Pressure, to be sure, but the variance in human-habitable environments isn’t high

[4] and the bad people, of course.

[5] to reinforce my point about units. the figure on the Wikipedia page is first given in acre feet.

One Reply to “The Science of Science Ficton: Estimation”

  1. Stevie says:

    What if the poison were to be delivered by a fleet of aging but airworthy forest fire water bombers? People would assume some sort of training exercise or air show display, or maybe the insidious threat includes setting a forest fire too?

    *Does some googling*

    This one can deliver 11.5K gallons of water a go according to the blurb. You’d need two if my sums are right. http://www.10tanker.com/the-plane.html

    If the baddies were bankrolled properly by some international cartel this might not be as far-fetched as it might seem from oh alright it is stupid. As you were.

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