One of the more useful skills that you can gain is to become adept and order of magnitude estimation (you will amaze your friends and maybe even win money from them ...:) )

This skill will also allow you to think our your feet better and to develope a more quantitative view of any problem. This is probably the most useful skill you can learn in this class.

Today we will try a bunch of practice problems to hone our skills.

The basic rule set for doing an estimation problem is

1. Understand the problem and what is being asked

2. choose a set of consistent units

3. try to scale up a local example that your familiar with

4. devise an estimation plan

5. turn the crank on your plan

6. perform a reality check on your result this important step is often completely forgotten

To begin with, I will work out the procedure for estimating the number of grains of sand on all the world's ocean beaches. This will give you an example of how to approach these problems.

In general, the estimates made in this way are never off by more than a factor of 10, and are often good to a factor of 2.



To basically do this problem you essentially need to define the volume of a standard beach and then determine how many standard beaches are there on the planet?

Standard Beach Volume = width x length x depth

For width, its clearly larger then 1 meter, probably 10 meters, but probably not more than 100 meters. So pick W=50 meters

For depth, similar bounding range pick D=10 meters

Okay, so how long is a standard beach - hmm - no we have to think about that.


How long is a coastline? In principe the combined coastline of say North and South America is 1/2 the circumference of the Earth.

How many coastlines are there:

• West coast of NA and SA
• East coast of NA and SA
• West coast of Eurasia + Africa
• East coast of Eurasia + Africa
• Australia cost (not as long as a cicumference call it 1/2 of that)

One-half of a Circumference is 20 million meters (2x10⁷)

so the total volume, in cubic meters of sand is then
Width x Depth x Length

= 50 x 10 x 20 million x 4.5 =45 Billion cubic meters of beaches

one sand grain is about 1 cubic mm so that are 1 billion grains of sand per cubic mater.

Number of grains of sand is then 45 billion x 1 billion or 45 x 10¹⁸ grains of sand.

Now, there is one factor left out as a correction. What do you think it might be?