Friday, October 2, 2009

Fermi Problem Rules of Thumb Part # 1

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 ~ 8x10^4 sec
1 year ~ pix10^7 sec
1 story (in a high rise) ~ 10 feet

Some "things to know"

Population of planet ~ 7 billion
Population of the USA ~ 3x10^8 people
Population of NYC ~ 8 million
Density of water 1000 kg/m^3
Density of Air ~ 1.3 kg/m^3


Average energy output of resting human ~ 100 Watt
Time light takes to get to the Moon from the Earth ~ 1.3 seconds
Time light gets to Earth from Sun ~ 8.3 min.

That is good for now. =)

3 comments:

  1. Some of the of facts I had noticed previously (or forgot, inspite of being a physicist for so many years ;)) are i) Exp(3) ~ 20 ii) Sqrt(10) ~ Pi (this one is pretty cool) , iii ) 1 story ~ 10 ft . So thanks for those !

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  2. Now how's the average energy of a resting human calculated?

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  3. It is just a rule of thumb, based on studies of metabolic rates of a large group of people. Output can range around this depending on activity etc.
    If you want to do a quick and dirty, look at any food package and you will see a little blurb that says:
    "* Percent Daily Values are based on a 2,000 calorie diet. Your daily values may be higher or lower depending on your calorie needs."

    Now, a food calorie is not a "physics" calorie, but is 1000 physics calories.

    So, average caloric intake is about 2000000 cal a day.

    Power = Energy/Time
    Power = (2000000 cal/(60*60*24 sec) ~ 97 Watt

    So that gives you a quick and dirty power output of the average human being. =)

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