Critical Fermi Estimation Knowledge
December 10, 2017 11:53 AM   Subscribe

Fermi questions assume a baseline knowledge of certain order of magnitude numbers when getting started with the estimations. Which numbers do you find most important? Have you found an online resource with a list of numbers to keep handy?

People in NYC? Distance between two places? Etc.
posted by fredericsunday to Grab Bag (5 answers total) 4 users marked this as a favorite
For Fermi-style questions, I often find myself remembering that there are approximately 8 billion people on Earth and between 300 million and 350 million people in the United States.
posted by brainwane at 1:57 PM on December 10, 2017

This question is nearly impossible to answer because the entry point to many Fermi-style estimation problems is "one key fact I happen to know," and that one key fact rarely repeats but is based on a general breadth of knowledge/trivia. For example, I do a lot of this in engineering (especially in quick power/energy budget estimates) and I find myself coming back to a few handy facts (all very approximate):

Sunlight: 1kW/m^2 (noon, equator)
AA battery: just under 2Ah @ 1.5V
Very very good cyclist: 200W
Energy densities: hydrocarbons = 1000x batteries = 1000x mechanical storage
Typical efficiencies: BAD
... etc.

But that list changes completely in a different discipline, and is pretty personal to me (another person could get just as close starting with a different list - I remember mine because it's drawn directly from my own experience).
posted by range at 2:48 PM on December 10, 2017 [3 favorites]

The diameter of the Earth, the population of the Earth, and the speed of light seem to often be pretty useful when I'm spitballing Fermi type problems.

I also find that the pinnacles of human accomplishment are good to know, like that a 4 minute mile is extremely fast and a 2 hour marathon just out of reach. Or that the world deadlift record is exactly 500kg.
posted by 256 at 6:50 AM on December 11, 2017

The whole point of Fermi estimation is that you use things you already know. The skill is in working out which of the things you know can be applied in the context of the question. Like any skill, you get better with practise.

One of the finest examples of this is XKCD working out what a mole of moles would look like.

Let's try an example: How much does Saturn weigh? Well, it's less dense than a rocky planet, which would be about 3-4 tonnes per cubic metre. It's mostly made of cold gases. Air on Earth is a gas. Air has a density of 1kg per cubic metre. Let's drop the density of Saturn at the high end of the middle because its atmosphere will be mostly dense and it must have some metal in the centre. Let's say it's about 1000kg per cubic metre.

Now: How much Saturn is there? Well, it's basically the same size as Jupiter. Jupiter happens to be ten Earth radii across, so 1000 times the volume of Earth. It's about 17,000km from Sydney to London (according to my Frequent Flyer statement), so the Earth's circumference is about 40,000km.

That's all the numbers we need. 40,000 ~= 30,000 ~= pi * 10,000 means the radius of the Earth is about 5,000km. (c=2*pi*r)

Volume of the Earth is about (4*pi) * (5000 * 5000 * 5000). 4 * pi is close to ten, so that's 10 *125 * 1,000,000,000 which is a trillion near as makes no difference.

Now: sanity check: the Earth is a trillion cubic kilometres of rock, with a density of about 10 billion tonnes a cubic metre because it's iron. That's a mass of 10 billion trillion tonnes, or 100 billion trillion kilogrammes. Wow. Now, we had some under-estimates in there. 3 is not actually four. But the Earth isn't entirely iron, either.

Anyway. Earth weighs about 10^23 kg, apparently. That's based entirely on my frequent flyer statement and knowing that iron is very heavy.

So: Saturn: We said 1000 times the mass of the Earth.

I'm going with 10^26kg.

{Checks Wikipedia} Sacred shitballs I'm out by a factor of five.

I brought three facts to that fight: My frequent flyer statement, a good guess at the density of the Earth (out by a factor of three), that Jupiter is ten times the radius of Earth and knowing that Saturn is a gas giant, about the size of Jupiter. I guessed that Saturn is about the density of water.

Fermi estimating is not about *what* you know, it's about linking the things you know together.

Thank you. That was fun.

Now go and do some yourself.

How many violins are there in Germany?

How much gas to cars consume in the US every day?

How long would it take to swim the course of the Nile?
posted by Combat Wombat at 7:03 AM on December 11, 2017

Taken as a whole, a cooked cadaver would yield about 81,500 calories' worth of food, says James Cole, a lecturer on human origins at the University of Brighton in England. But that's only if you wolfed down every part that could be consumed.

Popular Science - Jun 27, 2014
posted by sebastienbailard at 12:25 AM on December 12, 2017

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