Estimation


Introduction to Estimation

Estimation is a useful skill for physicists and engineers. A reasonable estimate to a proposed problem can save a lot of work - for example could coal be used to power a space rocket? Work out roughly how much coal would be needed and the answer is no so don't bother trying.
Before starting a detailed and accurate calculation, an estimate of what the answer should be, allows for a 'sanity check' to make sure the final answer is not wildly wrong.

No one knows exactly how many stars there are in the galaxy - some say 100 billion and some say 200 billion. Neither of these answers is an exact number, one is twice as many as the other but they are both to the same order of magnitude ie 10 to the power 11. There is a large range of heights of people in the world but no one is less than 0.1m tall and no one is more than 10m tall so the order of magnitude for the height of people in the world is 1m.
Working with orders of magnitude makes estimations easy because we are just dealing with powers of ten.

Difficult or impossible calculations which can be estimated are named after Enrico Fermi who was famously brilliant at these type of calculations. Some people do Fermi problems just for fun and some people run competitions but practising these types of problems has two advantages: it improves your mental mathematical dexterity and it allows you to quickly check on whether your more detailed calculations are likely to be right or not.

Here is an example: How many litres of water are in Lake Windermere?

First we need the volume. 
Windermere is more than 10 km long but less than 100 km long so for the length we say 10
It is, on average, more than 100 m wide but not more than 10 000 m wide so for the width we say 10m
By a similar argument the average depth is likely to be 10m
The volume is therefore 10(4+3+2) m3 = 10m3
 
1m3 of water is equivalent to 1000 litres so Windermere contains 1012 litres of water.

Below are some more examples of Fermi problems and links to websites that offer more help in solving them.

If you find a particularly nice one or need help with a tricky problem, why not tweet it to @UVHSFermi ?






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Thomas Carl Pion,
Sep 12, 2015, 5:50 AM
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Thomas Carl Pion,
Sep 12, 2015, 5:50 AM
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Thomas Carl Pion,
Sep 12, 2015, 1:16 AM