Transcript Guesstimation: Solving the world`s problems on the back of a

Guesstimation:
Solving the world’s
problems on the back of a
cocktail napkin
Larry Weinstein
Old Dominion University
Princeton University Press, 2008
Jefferson Lab, 17 Sept 2008
Why estimate?
Answers lead to actions.
Answers fall in one of three ‘Goldilocks’ categories:
1) Too big
2) Too small
3) Just right (in the middle)
‘Too big’ or ‘Too small’ lead to obvious actions.
‘In the middle’ requires more thought (and perhaps even
actual calculation).
“An approximate number sense is essential
to brute survival”, Gut Instinct’s Surprising
Role in Math, NY Times, 16 Sept, 2008.
Jefferson Lab, 17 Sept 2008
How to estimate (almost) anything
1) Write down the answer (to within a factor of 10).
If you can establish lower and upper bounds, take
the geometric mean for your answer.
How many clowns can fit in a VW Bug?
More than 1 and less than 100.
Estimate = 1100 10
This ensures that your estimate will be within a factor
of 10.

2) If you can’t write down the answer, break the
question into smaller pieces and go to step 1
Dare to be imprecise!
Jefferson Lab, 17 Sept 2008
How much individual trash do Americans
generate every year?
Reality: 2108 tons of Municipal Solid Waste
How much landfill space will we need for
the next century’s trash?
V = 2108 tons/yr  102 yr / (1 ton/m3) > 21010 m3
Use V = 1011 m3.
Landfill is 100 m high and 109 m2 = 103 km2 in area
That is Los Angeles or Virginia Beach.
Jefferson Lab, 17 Sept 2008
Paper or plastic? What is the mass of
all the flimsy plastic bags you use each
year?
How does it compare to the mass of
gasoline you burn each year?
Jefferson Lab, 17 Sept 2008
If the Sun were made of gerbils, the Earth
would be incinerated. Compare the power
density of mammals and the sun.*
Humans:
P = 2500 kCal/day  (4103 J/kCal) / 105 s/day
= 100 W
Power/mass = 100 W / 100 kg = 1 W/kg
Sun:
P = 103 W/m2  4(1.51011 m) = 31026 W
M = 21030 kg (from orbital period of Earth)
Power/Mass = 10-4 W/kg
*Thanks to Brian Quinn for the question
Jefferson Lab, 17 Sept 2008
What is the energy density of gasoline?
Reality = 45 MJ/kg
What is the energy density of batteries?
Reality = 0.2 to 0.5 MJ/kg
What is the energy transfer rate of
gasoline (when fueling your car)?
Jefferson Lab, 17 Sept 2008
How much power can a windmill produce?
Reality: 92 m blade diameter wind turbine in a 11 m/s
wind would generate 2 MW (Danish Wind Energy Assc)
But: Power  wind speed cubed. Very variable!
Jefferson Lab, 17 Sept 2008
Summary
Write down the answer.
Break up the question if you need to.
Dare to be imprecise!
•Estimate to within a factor of 10
•Take the geometric mean of lower and
upper bounds
Remember a few key numbers:
•1 m/s ~ 2 mph
•Water density = 1 ton/m3 = 1 kg/liter
•Avogadro’s number = 61023
•US population = 3108
Jefferson Lab, 17 Sept 2008