### Fermi Problem Rules of Thumb Part # 1 (PC)

In order to do Fermi problems, and other back of the envelope calculations with confidence, one must have an few tricks and rules of thumb that can be brought out quickly.

In this entry into Fermi problem rules of thumb, I will introduce a few tricks.

Numbers:

Sqrt(20) ~ 4.5

Sqrt(10) ~ pi

Sqrt(3) ~ 1.7

Sqrt(2) ~ 1.4

2^5 = 32

2^10 ~ 1000

Exp(3) ~ 20

Exp(1) ~ 2.7

Example: (Taken from Back of the Envelope Physics, Clifford Swartz)

Exp(40)= e(e^3)^13 ~ e(20)^13 ~ e(2)^13 *10^13 ~ 2*10^17

Exp(40) = 2.35x10^17 Close enough.

Some Conversions:

1 mi/h ~ 1.5 ft/s ~ 1.6 km/h ~ 0.5 m/s

1km/h ~ 0.3 m/s ~ 0.6 mi/h

1 ft/s ~ 0.3 m/s ~ 1km/h ~ 0.7 mi/h

1 m/s ~ 3.3 ft/s ~ 2.2 mi/h

1 day ~ 8x104 sec

1 year ~ pix10^7 sec

Some "things to know"

Population of the USA ~ 3x10^8 people

Population of NYC ~ 8 million

Density of water 1000 kg/m^3

That is good for now. =)

In this entry into Fermi problem rules of thumb, I will introduce a few tricks.

Numbers:

Sqrt(20) ~ 4.5

Sqrt(10) ~ pi

Sqrt(3) ~ 1.7

Sqrt(2) ~ 1.4

2^5 = 32

2^10 ~ 1000

Exp(3) ~ 20

Exp(1) ~ 2.7

Example: (Taken from Back of the Envelope Physics, Clifford Swartz)

Exp(40)= e(e^3)^13 ~ e(20)^13 ~ e(2)^13 *10^13 ~ 2*10^17

Exp(40) = 2.35x10^17 Close enough.

Some Conversions:

1 mi/h ~ 1.5 ft/s ~ 1.6 km/h ~ 0.5 m/s

1km/h ~ 0.3 m/s ~ 0.6 mi/h

1 ft/s ~ 0.3 m/s ~ 1km/h ~ 0.7 mi/h

1 m/s ~ 3.3 ft/s ~ 2.2 mi/h

1 day ~ 8x104 sec

1 year ~ pix10^7 sec

Some "things to know"

Population of the USA ~ 3x10^8 people

Population of NYC ~ 8 million

Density of water 1000 kg/m^3

That is good for now. =)

Labels: Fermi Problem, Rules of Thumb