Orders of Magnitude

Fermi Estimates and Understanding Numbers

This was my idea of a Fermi Question: Turn every experience into a question. Can you analyze it?

If not, you'll learn something. If you can, you'll also learn something.

- Philip Morrison, Ph.D.

Enrico Fermi (1901-1954)

• Born in Italy• Earned Ph.D. in physics at the age of

21.• Received Nobel Prize in 1938, for work

on “Artificial Radioactivity Produced by Neutron Bombardment”.

• Emigrated to U.S. in 1938, mostly to escape the fascist regime of Mussolini.

• Lead work in Chicago which resulted in the first controlled nuclear reaction.– This ultimately lead to the development

of the atomic bomb.• In 1944 became an American citizen.• Died in Chicago in 1954.• Today the Fermi National Accelerator

Laboratory in Batavia, IL is named after him.

Sources: http://nobelprize.org/nobel_prizes/physics/laureates/1938/fermi-bio.htmlhttp://www.lanl.gov/history/atomicbomb/pdf/Enrico%20Fermis%20Observations%20at%20Trinity,%20July%2016,%201945.pdfhttp://larrycalloway.com/trinity-tes

Time and Distance

"How many piano tuners are there in Chicago?"• To start you have to make some reasonable guesses.

– Approximately 5,000,000 people living in Chicago. – On average, there are two persons in each household in Chicago. – Roughly one household in twenty has a piano that is tuned regularly. – Pianos that are tuned regularly are tuned on average about once per year. – It takes a piano tuner about two hours to tune a piano, including travel time. – Each piano tuner works eight hours in a day, five days in a week, and 50 weeks

in a year. • From these assumptions we can compute that the number of piano tunings

in a single year in Chicago is:

Source: http://en.wikipedia.org/wiki/Fermi_problem

5,000,000 persons in Chicago 1 piano 1 piano tuning piano tunings in Chicago2 persons/household 20 households piano year year( ) 125,000

5 days 1 piano tuning piano tunings50 weeks 8 hoursyear week day 2 hours piano tuner year piano tuner/ 1000

piano tunings in Chicagoyear

piano tuningsyear piano tuner

125,000

1000125 piano tuners in Chicago

Sources: N. Angier, The Biggest of Puzzles Brought Down to Size, The New York Times, 2009

http://www.nytimes.com/2009/03/31/science/31angi.html Weinstein and Adam, guesstimation, 2008

1 mile ~ 1.6 km

Need:• Diameter of golf ball.• Circumference of earth.

Circumference of earthDiameter of golf ball# of golf balls =

1 inch ~ 2.5 cm

The diameter of golf ball is ~1.5 inches or ~4 cm

The circumference of the Earth is a little more tricky.If you can remember it or the Earth’s radius great, but I never do.

But I do remember that it is about 3,000 miles from the east coast to the west coast and that is about 1/8 the distance around the earth.

So the circumference is ~ 24,000 miles or ~40,000 km

3 24 9Circumference of earth

Diameter of golf ball

10 m 1 golf ball 10 cm# of golf balls = 4 10 km 10 golf balls

1 km 4 cm 1 m

2 29

29 2 3 2

6

1 m 1 km6 10 people 10 10

6 peoplem

10k

mm

~33 km or ~ 20 mi

~33

km

or

~ 2

0 m

i