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Jefferson Lab, 17 Sept 2008 Guesstimation: Solving the world’s problems on the back of a cocktail napkin Larry Weinstein Old Dominion University Princeton University Press, 2008

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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.

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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 = 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!

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Jefferson Lab, 17 Sept 2008 How much individual trash do Americans generate every year? How much landfill space will we need for the next century’s trash? Reality: 2 10 8 tons of Municipal Solid Waste V = 2 10 8 tons/yr 10 2 yr / (1 ton/m 3 ) > 2 10 10 m 3 Use V = 10 11 m 3. Landfill is 100 m high and 10 9 m 2 = 10 3 km 2 in area That is Los Angeles or Virginia Beach.

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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?

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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 10 3 J/kCal) / 10 5 s/day = 100 W Power/mass = 100 W / 100 kg = 1 W/kg Sun: P = 10 3 W/m 2 4 (1.5 10 11 m) = 3 10 26 W M = 2 10 30 kg (from orbital period of Earth) Power/Mass = 10 -4 W/kg *Thanks to Brian Quinn for the question

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Jefferson Lab, 17 Sept 2008 What is the energy density of gasoline? What is the energy density of batteries? What is the energy transfer rate of gasoline (when fueling your car)? Reality = 45 MJ/kg Reality = 0.2 to 0.5 MJ/kg

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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!

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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/m 3 = 1 kg/liter Avogadro’s number = 6 10 23 US population = 3 10 8

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