Cumberland Times-News

Columns

November 10, 2012

Here’s how you figure out what’s left behind

To most adults, an estimate is the amount of money that house repair or car repair will likely cost you. These estimates are made by a house repair person or someone in the service department of your car dealer.

But there are many questions about nature, our way of life and sky bodies that can be investigated by high school mathematics. Why I decided to write this column was the publication of “Guesstimation 2.0” by Lawrence Weinstein.

This book is a Princeton University paperback with ISBN 978-0-691-15080-2. It is a sequel to “Guesstimation” by the same author.

What kind of estimates does Weinstein do in this book? Here are a few questions in this book: How far would all the rolls of toilet paper used in the U.S. in a year stretch? How high would a stack of a trillion paper dollar bills be?

And How does the volume of all man made structures in the U.S. compare with the volume of Mount Everest?

Here are some basics of estimation. Most estimates are based on considering the frequency of events over a certain period. To find the frequency, we need to come up with some reasonable factors.

Each factor may be either a bit high or a bit low, but when you multiply them together, they tend to offset each other.

An example can be quite helpful in understand estimation. Here’s an example from my summer time physics class. It’s about something that most of us have to deal with, bird excrement (poop) on our cars or light trucks.

Some of us try to clean it up quickly while others (myself included), wait for the next good rain to wash it off. (My car is rather old and not the sleek, shiny car I bought 13 years ago.) Let’s consider a day in spring or fall when flocks of migrating birds fly over Cumberland.

The estimate I seek is how many pounds of bird poop land on all the personal vehicles in Cumberland each day.

First, we have to estimate the number of birds that spend the better part of day over our fair city. From what I’ve seen (hundreds of birds in view at a time), I estimate that perhaps 10,000 birds spend significant time over Cumberland in one day.

How many times a day do birds drop their wastes? Birds often eat worms, garbage, road kill (just the bigger birds), bird seed, and also drink out of puddles, bird baths, water bowls set out for dogs, etc.

I mention drinking as birds drop a mix of liquid and solid wastes at the same time as they fly. To me, it seems reasonable that a typical bird may void 10 times a day as they fly. What is the weight of an average bird drop? I estimate 0.01 pounds per deposit.

So with these numbers, we can get a total amount of bird excrement dropped on Cumberland. We must multiply the number of birds times the number of drops times the weight of each drop. This is 10,000 x 10 x 0.01 = 1,000 pounds!

Now how much of this stuff lands on cars or light trucks? On any one day, there may be 10,000 of these vehicles either parked or in motion in the city of Cumberland. (These are not just the cars or light trucks of Cumberland residents but also owned by commuters from nearby Maryland towns and Pennsylvania and West Virginia.)

Cumberland can be approximated as a rectangle that’s 15,000 feet E-W and 10,000 feet N-S. Then the area of Cumberland would be 150 million square feet. A typical motor vehicle may be 15 feet long and 6 feet wide or about 100 square feet.

So the total area of cars/light trucks would be 100 square feet x 10,000 vehicles or 1 million square feet.

The last step is to multiply the total load of bird poop by the fraction of the area covered by Cumberland light vehicles. So 1000 pounds x 1 million /150 million = 6.67 pounds of bird droppings each day.

Future columns will treat some more estimates involving sky objects and money.

SKY SIGHTS AHEAD: Later this week, the moon will return to the evening dusk. On Thursday, a slender crescent moon will be seen quite low in the southwestern 5:45 p.m. dusk. To the left of the moon at that time will be the planet Mars.

On Friday, the moon will appear above and to the left of Mars. Mars is now rather dim, being on the far side of its orbit. On Saturday at 6 a.m., the brilliant planet Venus will appear above Spica, the brightest star of Virgo.

Bob Doyle invites any readers comments and questions. E-mail him at rdoyle@frostburg.edu. He is available as a speaker on his column topics.

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