How many leaves fall in Dublin every autumn?

It's an impossible question to answer, right? And even if it is possible to answer, you'd probably need a mathematical formula that you either don’t know or that is far too complicated.

Well, not necessarily.

While it might be impractical to count the exact number of leaves that fall in Dublin each year, a physicist can approach a problem like this and break it down into manageable, logical sections and come up with an answer.

We call this sort of question a Fermi problem.

Enrico Fermi

Enrico Fermi was an Italian physicist, celebrated for his work on quantum theory, nuclear physics and statistical mechanics.

We call the type of solution to the problem we’re looking at here the Fermi method, because of Fermi's ability to come up with quick, accurate answers to mathematical questions that would confound other people. He once used the Fermi method to estimate the yield of an atomic bomb tested in 1945 at the White Sands Proving Range, New Mexico. He dropped paper from his hands at the edge of the blast area, and made his calculations based on how far the paper traveled during the explosion.

Fermi is often called the the father of the atomic bomb, but would he later argue against the development and advancement of nuclear weapons.

Let’s have a go at getting an answer to our leaves question.

We've broken the problem down into logical steps for you already, so just fill in the values that you think are right.

Assumptions

To get an answer, you’ll need to make assumptions at every stage.

We often think of science as definitive or absolute but scientists often rely on assumption and estimation.

It is their ability to quantify uncertainty that matters. If you wish to increase the accuracy of your answer, then you can be more exact in your estimation. Sometimes the need for the accuracy of the final figure depends on how you intend to use it. Estimating the size of a crowd for a newspaper report might be important but estimating the forces that a commercial jetliner might experience in flight could be more so.

Estimation is an essential part of this type of problem solving

So don't worry about not knowing the correct response. Make your best estimate and lets figure out how many leaves fall in Dublin every autumn.

Method

A big part of finding a solution to a Fermi problem is deciding what questions need to be asked.

In this example we've provided the steps – thinking of Dublin as a semi-circle, estimating the amount of land covered in trees, that sort of thing – but this is just our solution. There could be other approaches, and some may be even better than the one that we’ve proposed.

Dublin is shaped like a half circle with a 25km radius. So its area is 981,000,000m2 – (1/2)πr2

1
How much of Dublin's land is covered by trees?
0%
100%
2
How many of these trees are deciduous (not evergreen)?
0%
100%

Imagine a typical tree...

3
How tall is the leafy bit of an average tree?
1m
100m
4
How wide is the leafy bit of an average tree?
1m
50m
5
How many leaves are there in 1m3 of the tree?
1
100,000
Calculate!

Given your responses...

An average tree has a footprint of XXXm2.
An average tree has a volume of XXXm3.
There are XXX leaves on an average tree.
There are XXX deciduous trees in Dublin.

Which means the answer to your Fermi problem is:

answer here

leaves fall in autumn in Dublin!

Head to our blog to find more Fermi problems and try them out from scratch yourself.