Feature: word problems

@ April 20, 2009

OC tipper yaworm writes (for, it would seem, the express purpose of enraging me):

Courtesy of the Wall Street Journal Online, the plight of $250,000/yr households finally has a voice.  If nothing else, read the second to last paragraph ("For the Parnells..."). Math!
The paragraph is reproduced for you here:

For the Parnells, their perception of themselves is based on the math. The value of their house is down $60,000. Ms. Parnell says the couple's gross income last year was about $260,000. Taxes, premiums for medical care and deductions for Social Security and their 401(k) contributions cut the gross to about $12,000 per month. The family tithes $1,300 a month at their church. Their mortgage, second mortgage and payment on land they bought is nearly $4,000 a month. Other expenses, including their family car payment, insurance and college funds, as well as basics like food, utilities and donations to charities, leave them with about $1,200 left over each month.
Only $1,200 left over each month after every tax has been paid, 401(k) contribution made, mortgages (plural) paid off, $1,300 given to their church, and all other mandatory expenses, including car payments, college funds, food, utilities, and other basics like donating to charities! Only! ONLY!! DO YOU KNOW WHAT ONLY MEANS YOU DOUCHE!

See... okay, I should calm down. Remember that scene in Pulp Fiction, when they had to shoot Uma Thurman directly in the heart with a shot of adrenaline? Well, if ever I'm in cardiac arrest, and you don't have a needle full of adrenaline handy, just read me that paragraph. I will instantly spring to my feet and punch you in the face.

@ April 2, 2009

Tesla Motors has finally unveiled their Model S, an all-electric sedan.  This is the long-awaited follow-up to the Tesla Roadster, their souped-up all electric sports car (with the souped-up price tag to match) that made a splash on the red carpet at the 2007 Oscars, and was never heard from again.  A work colleague asked this question:

Can someone help me understand how charging an electric car with power generated from a coal-fired plant is a good thing? I understand that CO2 emissions from gasoline internal combustion engines are less than coal-fired power plant emissions.  I get the part about buying oil from foreign countries, I'm just talking about net-net emissions.
Ignoring for a moment that this person with an engineering degree was unable to do the math themselves, let's take a look.

@ March 6, 2009


"A 63-year-old attorney based in Lafayette, La., who asked not to be named, told ABCNews.com that she plans to cut back on her business to get her annual income under the quarter million mark should the Obama tax plan be passed by Congress and become law.

"We are going to try to figure out how to make our income $249,999.00," she said."

Current marginal tax rate for the highest earners: 33%

Proposed marginal tax rate for highest earners in the Obama plan: 36%

Before the math, a hypothetical: does this constitute class warfare? Find the answer at the end of the column.

Now, a math question. You earn $255,500, placing you in the top tax bracket of 33%. The rates for this bracket increase to 36%. Barring any other changes in the tax code, how much does your tax bill increase?

Here is the math that people like Unnamed 63-Year-Old Attorney appear to be doing:

$255,500 * (36% - 33%) = $7,665

Oh god! That brings you below $250,000! That means you are being penalized for making more! Class warfare! CLASS WARFARE!!

Here is the problem: you, Unnamed 63-Year-Old Attorney, are an idiot. I hope for the love of god you aren't a tax attorney. Here is how the math actually looks:

($255,500 - $250,000) * (36%-33%) = $165

That's right, boys and girls: the money you earn gets taxed based on the bracket it belongs in. An example: If the tax rate up to $50,000 is 20%, up to $100,000 is 25%, up to $250,000 is 30%, and over is 35%, then people who earn over $250,000 get their taxes calculated, not like this:

Income * 35% = tax bill

It gets calculated like this:

$50,000 * 20% + ($100,000 - $50,000) * 25% + ($250,000 - $100,000) * 30% + (Income - $250,000) * 35% = tax bill

The thing is, I'm betting all of you know that, because you aren't learning disabled like Unnamed 63-Year-Old Attorney. The real question here isn't how to solve the math problem, but rather: why do we have a news story from a major outlet like ABC News about people like this that isn't focused on how they are retarded and our underfunded educational system has failed them? It's like reading a piece of hard-nosed investigative journalism about where did Frankie's ball go. IT IS UNDER THE COUCH FRANKIE.

(The answer to the hypothetical: 36% tax rates only quantify as class warfare if you believe that we were engaged in class warfare during the 1990s before the Bush tax cuts. But the politics are really a story for another day.)

(Okay, this reminds me of something else: last time I was home during the day, I was watching an episode of Maury where a man vehemently denied paternity of his girlfriend's child because she was unfaithful to him. Right before they cut to his testimonial video, she shouts at him, "Yeah but it was with a woman!" and his face, which is on a big screen right behind Maury as he tosses to the video, is completely stunned: "Oh I didn't know that" he mutters right before we get a video telling us all about he ain't the father of DeShawn. He spends the rest of the segment feeling incredibly contrite and embarrassed as Maury goes through the motions before revealing that YOU ARE THE FATHER. That's what should have happened to this story: the reporter should have told the attorney that the tax increase would only apply to that portion of their earnings above $250,000, followed by a quick, embarrassed, "Oh I didn't know that.")

@ December 22, 2008

On Friday, I accused Drew Carey of retroactively ruining my childhood with his incredibly underwhelmed reaction to an exactly perfect bid on a showcase.  OC tipper Jim accuses that bidder of cheating:

"While it is legal to hear bid ideas from audience members, on that September 22, 2008 taping, CBS Standards and Practices and host Drew Carey were both suspicious of some audience members during the bidding. As a result, there was a 45-minute shutdown between the Showcase presentation and reveal on that taping. Some in the audience noted Carey's cold, subdued reveal of what should have been one of the show's most historic moments was related to the suspicion that the production staff had on the win."

So what of it? Did Terry Kneiss, the Perfect Bidder, actually cheat?

Presumably, the only evidence of cheating is the bid itself.  Perfect.  Also, incredibly unlikely, as revealed by the fact that nobody had ever done it before.  But is this evidence in and of itself incriminating enough?

Jim, in his comments, notes that there have been previous winners who were as close as $1 to the actual retail price.  I would also make the following observations:

- If Mr. Kneiss had previous knowledge of the bid prices, I would expect him to bid slightly under the actual retail price, rather than the exact retail price, for fear of drawing suspicion on himself.  Why risk an exact bid?

- Mr. Kneiss was in the second position, meaning he could not know ahead of time which showcase he would be bidding on.  He would then have needed advanced knowledge of both showcase prices.

Instead of using the bid as prima facie evidence of Mr. Kneiss' guilt, let's examine that claim further.  What are the odds of getting a showcase bid exactly right?

For this analysis, we will make some assumptions.

- Any person getting to the showcase showdown will be a reasonably skilled bidder. As such, his bids will generally be within +/- $10,000 of the actual retail price.

- Bidders are much more likely to bid a round number (say, $25,000 instead of $25,162).  I will estimate that 3 out of 4 bidders guess round numbers. 

If a typical Price Is Right showcase bidder is able to get within a $20,000 range of the actual retail price, that makes the initial odds 1 out of 20,000 that the bid will be exactly right.  If we further weight the bids such that a round number (say, $1000 increments) are more likely to be bid by a 3:1 margin, the odds drop.  If, say, the value is $25,162, and there is only a 25% chance you will even bid a number that is not an increment of $1000, then the odds shift accordingly, from 1 in 20,000 to 1 in 80,000.

These are long odds, but they are not ridiculous.

Consider: there have been 7,000 episodes of the show taped so far, with 2 showcase bids each show, for a total of 14,000.  That is 14,000 chances for an exact bid. 

Every instance there is a bid, the odds are 79,999 out of 80,000 that it will not be exactly right.  If this process 14,000 times, the odds of no exact bid ever occuring are:

(79,999/80,000)^14,000 = 84%

That means that, after 14,000 instances, there is a 16% chance that an exact bid HAD occurred.  Unlikely, but not zero.  Any event which has a non-zero probability of happening, however small, will eventually happen if given enough chances.  That is why, despite odds of 100 million to one against, somebody eventually wins the Powerball after enough tickets are sold.  Terry Kneiss is the vessel by which the hands of fate showed The Price Is Right viewers the power of infinity. 

And Drew Carey? That motherfucker RUINED MY CHILDHOOD.

@ August 29, 2008

Before watching Obama's speech last night, I was on the phone with my mom.  My mom does not like Barack.  She is not a Barack supporter.  She is one of those Hillary supporter's you hear about that don't want to vote for Barack for some crazy reason or another.  "He's an empty suit," she says.  "Change? What does that mean? It's all empty rhetoric," she says. "No, it's not because I'm a bitter, bitter woman," she says.

I think Obama might have overheard our conversation, because about halfway through his speech, he said this: "So let me spell out exactly what that change would mean if I am President."

He then proceeded to run down a laundry list of specific policy positions that embody his idea of "Change." Because I am an obsessive one-issue voter, I zoned in on this part of the speech:

"[I]n ten years, we will finally end our dependence on oil from the Middle East."  

More empty rhetoric, or actually possible?

Let's look carefully at what he said.  He is not promising to eliminate our dependence on oil, or even our dependence on foreign oil.  He is specifically pledging to eliminate oil imports from the Middle East.

(Quick aside: I suspect in the next day or so we'll see a clarification that says he wants to eliminate oil consumption equal to that of current Middle East import levels, as opposed to any type of import embargo from these countries.  Stay tuned.)

Here is a helpful quote from the AP on this issue:

"Last year, the United States imported about 10 million barrels of oil a day, of which about 20 percent came from the Persian Gulf states."
To eliminate Middle East oil imports, we would need to reduce imports by 2 million barrels of oil every day.  Guess what?  We don't need any new untested technology, or to all buy electric cars, or to start bike commuting.  This is completely achievable through increased fuel efficiency standards alone.

The average American uses 500 gallons of gas every year to travel 12000 miles, or an average of 24 miles per gallon.  A reduction of 2 million barrels a day, at 42 gallons per barrel, translates into a per-American reduction of about 110 gallons.  390 gallons to travel those same 12000 miles yields a fuel efficiency of 31 miles per gallon.

Obama could have said, "In 10 years, we will end our dependence on oil." Period.  Al Gore said something similar recently (he actually called for an end to dependence on all fossil fuels, not just oil).  That is an honorable goal, and a desirable goal, but in the real world, it does not appear to be an achievable goal. 

In fact, here is someone saying that he set the bar too low.  Here's another that says he set the bar too high.  That makes me think he got it just right.

@ August 6, 2008

You knew this was coming.

Obama sez: Drilling = fail, keeps ur tires inflated for gas savings bonanza!
McCain sez: LOL, what a joke, drilling FTW!

So, is Obama out of his mind? Can proper tire inflation really save as much oil as we could get from all the proposed offshore drilling?

Recall from the previous Word Problems article you most likely didn't read that, at peak production (which would be anywhere from 10-20 years from now under any reasonable scenario), drilling from both the offshore sites and ANWR would pump about 2 million barrels of oil into the market every day against the 20 million barrels we use.

Now we have our benchmark, time for the hard part: how much oil could we really save with proper tire inflation and regular tune-ups?

This isn't research I'm prepared to do.  Thankfully, the good folks over at the Department of Energy have done it for us on this website:

Properly inflating your tires is good for an additional 3% on your vehicle's fuel efficiency.  A properly tuned engine is good for another 4%.  A clogged air filter could be a 10% hit.  And even the wrong motor oil can give you a 2% improvement.

Taken together, these car maintenance conservation techniques could save a worst-case driver 15%.  Here, I'll throw a dart at a dartboard and call it at 5% improvement for the average driver

The savings from tire gauges and car maintenance is slightly smaller than the 10% increase in available oil from the potential drilling, with one little caveat. Inflate your tires now, and you get the savings now.  Start drilling right here, right now, and the savings don't start for a decade

(Can we pause here so I can laugh at the spectacle of politicians insisting that Congress return from vacation to vote on drilling? Yeah, that 5 weeks is really going to make a difference moving forward with an energy plan that has a 10-20 year lead time.  Does this bullshit really fool people?)

Unfortunately, it looks like this oil drilling talk is starting to take hold.  According to recent surveys, 70% of Americans are in favor of more drilling.  While I don't think it will solve any problems, and may result in an environmental disaster in the Gulf  and/or the Alaskan wildlife refuge, that really is an environmental question, not an energy question.

Looking at it through the prism of achieving energy sustainability, and putting aside any environmental concerns: I say let 'em drill.  Drill to your hearts content, motherfuckers.  Drill in the Gulf, drill in ANWR, drill for oil in Teddy Roosevelt's head if you think it's there. Because, eventually, there won't be anymore places to drill for oil in, no more magic beans that would solve everything if mean old Nancy Pelosi would just let the American people have them.  The excuses will run out, and the price of gas will be as high as ever.  And then maybe, just maybe, we'll be able to make some progress, instead of this childish horseshit.
tire gauge.jpg

@ July 14, 2008

Or, put it another way: "Bush to lift executive ban on offshore oil drilling"

It occurs to me that the "Word Problems" feature may seem as a way for me to apply my lefty-leaning politics to current issues under the guise of objectiveness, Sophie cheating at battleship notwithstanding.  If it appears that way to you, might I suggest: my choice of topic certainly comes out of my tree-hugging commie bias, but numbers be what they be, motherfucker.

So: should we get drillin'?

Guidance from our politicians on this issue is shaky at best.  Bush has been pro-drilling for about as long as he's been the son of an oil-millionaire - difficult to accept his opinion on face value, even if he wasn't, you know... stupid.

(Quick aside: I don't think Frank Caliendo is funny, but isn't it amazing that DirecTV is actually using his impression of the president as a fool who is astonished by the functioning of a television remote as a way of promoting their product? Has anything ever happened like that before with a sitting president?)

(Jesus Christ.  2 terms, people.  Anyway, where was I...)

So instead of looking to the current pres for guidance, let's look at the stances of the two politicians looking to replace him.  John McCain was long an opponent of offshore drilling, but has recently changed his stance to pro-drilling.  However, as you heard here first, McCain has recently been dried and hollowed out so that George Bush can crawl inside and control his actions like the alien in the first Men In Black movie.  So, we can't trust him.

Obama is anti-drilling, but, as a secret Muslim, he would obviously take that stance since increased oil production stateside would interfere with the operations of his Arab overlords.  Can't trust him, either.

No choice - we have to go to the numbers. (Note: if you don't actually want to see the numbers, just skip to the end.  Srs bizness!!)

Unless you are an oil company executive, your decision on a pro/anti drilling stance should be made on whether or not you think taking these actions will help bring down the price at the pump.  Let's break it down: the question of "should we drill offshore and in the Alaskan National Wildlife Reserve (ANWR)" becomes "how much more oil will we get, how much will that bring down the cost of oil, and how much does the price of oil affect the price of gasoline?"

How much more oil will we get?

In the ANWR, about 10.5 billion barrels. Peak oil production would be 800,000-900,000 barrels a day... sometime after 2020.

Offshore, about 16 billion barrels would be opened up. Peak production would be on a similar scale and timeframe.

How much will that bring down the cost of oil?

I'm not an economist, and I don't feel like building a supply-demand curve to figure this out the right way.  So, I'm going to fudge a little bit.

The US currently consumes 20 million barrels of oil every day, give or take. Let's give the ANWR and offshore fields the benefit of the doubt, and say we'll get a total of 2 million barrels of oil every day, once they hit peak production - this will happen many years from now, but, again, I'm going to make this simple, so let's assume it happened right now, today.  Oil costs $140 per barrel.  If there was an extra 2 million barrels on the market, let's say this drops the price of oil by 10%. 

How much does the price of oil affect the price of gasoline?

Why, that is an excellent question.  Thank you for bringing it up!

To determine this, we will explore some historical prices.  Let's look at the national average price of both oil and gasoline today, 5 years ago, and 10 years ago. (Costs are per barrel/per gallon)

2008:  $140/$4.12
2003:  $28/$1.78
1998:  $12/$1.17

From 98-03, oil went up by a factor of 2.3, while gas prices went up by a factor of 1.5.  From 98-08, oil went up by a factor of 11.7, while gas only went up by a factor of 3.5. 

On other words: the price of oil goes up much faster than the price of gasoline.  Whaaa? That's right: there are other factors in the price of gasoline other than how much the oil costs.  A 10% reduction in oil cost does NOT translate into a 10% reduction in gasoline costs.  Refinery costs and capacity make up a very large part of the cost of a gallon of gasoline (that is why after Hurricane Katrina, gasoline prices spiked dramatically - refining capacity nationwide was hit hard by the storm, in addition to some black people.) 

From a typical barrel of oil, depending on the refining process used, you get 20 gallons of gasoline (the rest of the oil goes to make jet fuel, heating oil, and the salve Dick Cheney soaks in every night to stay alive).  At $140 per 42-gallon barrel, oil costs $3.33 per gallon.  Reducing the cost of oil by 10% would result in a per gallon of oil savings of about 33 cents per gallon.


If the ANWR and the Gulf Coast fields were at full capacity today, we'd save something like 30-40 cents on every gallon of gasoline.  Of course, full capacity won't be reached for 10 years at the earliest - who knows how high the price of gasoline will be by then.  30-40 cents will be a drop in the bucket against $6-7 per gallon. 

At $140 per barrel, though, there is money to be made.  Offshore drilling becomes profitable at about $60 per barrel.  With a profit of $80 per barrel, the oil in the Gulf alone is worth $1.2 trillion dollars.

Like I said, the choice of whether to drill is up to you.  Just know what you are getting out of it (30-40 cents off a gallon of gasoline), and what the cost might be.

@ May 7, 2008

Okay, enough of the preachy environmentalist stuff.  I have a real problem, sent to me from Cousin Eric:

We all know  the game Battleship, but Sophie has taken it to another level in an unheard of episode of beginners luck.
The past few weeks Sophie has graduated from Dominoes and Candyland to Trouble (with the pop-o-matic) and now Battleship. She's not fared too well with Trouble, but is undefeated (5-0) in Battleship and on Sunday she took the game to a new level, one that I have never seen before (and I've been playing since the 1960's).   It took Sophie only 18 turns get the 16 hits to sink my entire fleet!  With 100 pegs on the board and only 16 hits available to opposing players the odds of getting one hit at the beginning of the game is 6.25 to 1 or the obvious 16%.  The odds change slightly as each player takes a turn, but the odds of hitting all the other players ships in only 18 turns is.....I have no idea, but it's pretty crazy!
Was there foul play involved?  I can find no evidence.  Sophie's Aunt Laury was in the room at the time, but she was on Sophie's side of the room and board.  Also, if Sophie was getting my coordinates from a Sophie sympathizer  (Laury, Molly, Rose or even Otis), at not yet 5 years of age her poker face has not yet evolved to keep this intel to herself. So, all I can conclude is this unprecedented once in a lifetime Battleship rout is legit and thought this was news worthy enough to share it with you.
The picture below was taken right after the final shot was fired.

Wow.  16 out of 18 hits.  Is this possible?  No, because it actually takes 17 hits to sink everything.  But 17 out of 19 hits? Is THIS possible?  Yes, obviously, it is possible.  That's a dumb question.  The real question is: what are the odds? Aha! Time for math! (PS: I really need to get back to work)

We calculate the odds by calculating, after each turn, the likelihood of getting another hit.  If the previous hit sank a ship, or this is the first shot, we calculate the odds of hitting a ship as (remaining open pegs in a ship)/(total pegs remaining).  In Eric's example above, at the beginning of the game, there are 17 possible spots to hit a ship, and 100 total pegs, so the odds of hitting a ship are 17%.  If the carrier is sunk, these odds change to 12/95, or 12.6%. 

If the previous hit did not sink a ship, then the odds will be calculated depending on the number of pegs already in the ship, the type of ship we are trying to sink, and the position of that ship on the board.  We will work through the carrier as an example. 

You have just hit a ship.  It is the carrier, although you have no way of knowing this.  You just see a peg sticking out of the board.  Your next move is to choose one of the 4 surrounding peg locations.  What are your odds of hitting again?

The carrier has five locations.  If you have hit either end of the carrier to start, your odds are 1/4.  If you hit somewhere in the center, your odds are 2/4, or 1/2.  So, your chances of hitting again are (1/4 + 1/2 + 1/2 + 1/2 + 1/4) / 5 = 40%.

battleship-first-hit.jpgNow you have two locations hit.  What are your odds of hitting a third time? If the two hits are at the ends, the chances are 1/2.  If the two hits are in the center, your odds are actually 100%.  (1/2 + 1 + 1 + 1/2) / 4 = 75%.

battleship-second-hit.jpgFourth time? (1/2 + 1 + 1/2) / 3 = 67%.

Fifth time?? (1/2 + 1/2) / 2 = 50%.

Now, we can calculate the odds of wiping out the cruiser without a miss, once you get that first hit: (0.4 * 0.75 * 0.67 * 0.5) = 10.05%.

If the ship is butted up against an edge, these odds are modified.

So, how do we distill all these facts down into the odds of this specific outcome? With computers! First, we look at the picture again, and assign each ship a position type: center of the board, longways against edge, shortways against edge, or corner.

carrier: center of board
battleship: center of board
submarine: center of board
destroyer: longways against edge
patrol boat: corner

Next, we'll fire up ye olde computer to crank out the odds of successfully hitting everything without missing (we'll get to the issue of the two misses in a second).

The odds of hitting all the spots without a single miss? 1.7 billion to one against.  Really.

Okay, so how do the two misses affect the outcome? Not much.  If we modify the original calculations so that there are 98 spaces to begin instead of 100, the odds drop to 1.5 billion to one against. 

Oh, Sophie, you had a good thing going with your 5-0 record, but clearly you got greedy. Buy that girl a deck of cards, Eric, because her poker face is better than you think. 

@ April 23, 2008

Previously, on ObscureBlog:

Ethanol sucks.  To be more specific, let's explore the effectiveness of ethanol as a renewable resource. 

Fundamentally, all energy, except for nuclear energy, comes from the sun (the great nuclear reactor in the sky).  Fossil fuels are a means of extracting solar energy that fell on the earth millions of years ago.  However, this solar energy reserve is running out.  We need to come up with ways of converting the solar energy that is falling onto the earth today into energy we can use without waiting the millions of years it takes for the generation of oil, coal, and natural gas beneath the earth.  Here are some numbers to start:

The intensity of solar radiation is 1 kW/m^2.  That means, if you had a 100% efficient solar converter, for every square meter of land it covered, you would get one kilowatt of power.   If that sunlight was collected for an hour, you would have one kilowatt-hour of energy.  Power is a measure of rate - how fast you've gone - and energy is a measure of quantity - how far you've gone.  With me so far?

However! This solar radiation is on a surface perpendicular to the sun.  If you have your collector on a flat surface at all times, you must correct for the incoming angle of the radiation.  This is why you are cold in the winter, when the sun angle is low, and warm in the summer, when the sun angle is high.  Science!

In addition to the effect of the angle of the incoming solar rays (called the "cosine effect"), you must also consider the length of each day and the typical amount of cloud cover in the area where your collector is located.  Fortunately, there is a government agency whose job it is to determine these things for us - the National Renewable Energy Laboratory.  Your tax dollars at work.

So, we can get all the information we need to calculate how much solar energy falls on the corn.  Now we need to know some things about corn.  Specifically:

When is it planted, and how long does it take to grow?
It depends on the area.  We are going to use Iowa as our test region, so we will say planting day is roughly on April 1st.  The time it takes to grow depends on the variety.  We will use 80 days as an estimate.

How much land is required to get us a single bushel?
In 2007, Iowa farmers harvested 2.5 billion bushels on 13.9 million acres, for a land-usage average of 180 bushels per acre.  Doing some math gets us to 1 bushel per 22.5 square meters.

How much ethanol do we get from a single bushel?
2.7 gallons per bushel, per the Department of Agriculture.
How much energy is in that amount of ethanol?
76,000 BTU per gallon, or roughly 60 kWh per bushel.


Let me pause here to make an observation.  Many people reading this by now will be completely confused; if they aren't confused yet, they will be by the end.  That is because energy is complicated unnecessarily.  Let's take a quick look at some of the power and energy units we encounter in our daily lives.

* Kilowatt hours (kWh) - this is how you are charged for electricity energy on your utility bill
* Therms - this is how you are charged for natural gas energy on your utility bill
* British Thermal Units (BTUs) - commonly used as a power rating for air conditioners
* Gallons of gasoline - energy you put into your car
* Barrels of oil - energy put into gasoline to put into your car
* Joules - standard metric unit for energy
* Erg - energy unit commonly found in crossword puzzles
* Horsepower - a unit of power used to rate car engines
* Calorie - energy unit used in food

If you want to be an educated consumer of energy, you should know what these (and other) units mean, and how they compare... I smell another Word Problem. Anyway, moving on.

We will use Des Moines, Iowa as our example location, since we used to only hear about ethanol subsidies at the beginning of each election cycle for the Iowa caucuses.  According to data from the Renewable Resource Data Center (a part of NREL), Des Moines, Iowa, typically sees 257.5 kWh per square meter for the 80-day period that starts on April 1st. 

All the hard work is done, so let's see what we get:

1 bushel requires 22.5 square meters.  If each square meter receives 257.5 kWh worth of solar energy, 1 bushel receives 5800 kWh.  From each bushel that is converted into ethanol, we get 60 kWh worth of energy.  This is a conversion efficiency of just over 1%. For comparison's sake, the worst solar panels - you know, the ones you refuse to put on your house because they are ugly - get 10%.  Corn is 10 times worse at converting sunlight into energy as the worst photovoltaics. 


@ April 22, 2008

Today's question: "Should we be using ethanol as a replacement fuel for oil?"

As it turns out, the "Word Problems column is becoming "Hippie Jesse and his Groovetactular Enviro-Mania".  Don't worry, I'm sure we'll fix the environment soon and I can move on to another topic to obsess over.  As for the question at hand: the answer is yes if you are a corn grower or oil company, no if you enjoy eating food.

The price of food is on the rise, and one of the causes could be biofuels, according to a UN expert and an Asian development bank.

Wait, wait, wait.  You are saying that if we stop using corn for food, and start using it to drive our trucks around, we're going to run out of corn to eat?

Uh, no shit.

This is where I would usually spend some space doing the math, but a little searching revealed that somebody had already done the work for me - last summer.  This excellent Slate article from last June, titled "The Great Corn Con," details everything that is wrong with trying use ethanol to replace oil as a transportation fuel.  Here are a few choice details:

"[Last June], the Senate passed an energy bill mandating the production of 36 billion gallons of ethanol per year by 2022--a sevenfold increase over current levels."

"According to the U.S. Department of Agriculture, distillers can produce about 2.7 gallons of ethanol per bushel of corn. In 2006, U.S. farmers produced about 10.5 billion bushels of the grain. So, even if Congress mandated that all of America's corn be turned into ethanol, it would yield only about 28.3 billion gallons, far less than the mandated volume."
I'm going to briefly pause here to re-iterate the author's point: all the corn in the United States cannot generate enough ethanol to meet the Congressional mandate in the last energy bill.  All the corn. ALL OF IT. WHAT THE FUCK ARE WE DOING, EVERYBODY.  Continuing:

"Thirty-six billion gallons of ethanol a year sounds like a lot, but it's only 2.34 million barrels per day. And given ethanol's lower heat content--about two-thirds that of gasoline--the effective production would be equivalent to 1.54 million barrels of oil per day. The United States uses nearly 21 million barrels of oil per day, of which 12.54 million barrels are imported. Thus, even if American ethanol producers can miraculously achieve the Senate's goal of 36 billion gallons per year by 2022, they will be producing the equivalent of just 7.4 percent of America's total current oil needs and just 12.2 percent of its imports. That quantity of ethanol will not take America very far toward the oft-repeated goal of energy independence."
I will repeat again: even IF we took ALL of the goddamn corn and made it into ethanol, we'd still only be displacing 12% of the oil that we import every year.  Sometimes I think Congress passes legislation just to fuck with me. 

So why does anyone even bother in the first place? What exactly is going on? If you ask me, it looks like a way for politicians to look like they are doing something for the environment without actually risking the status quo.  But what do I know, just because I can do basic arithmetic.  Let's move on, because there is another important reason that ethanol sucks more balls than the machine at the batting cages.

Oil, as you should know, is a fossil fuel.  There is only a certain amount in the earth, and once it is gone, it is gone forever.  However, ethanol is a renewable resource.  We can keep growing that corn.  But where does the energy in the corn come from? Like all (non-nuclear) energy, it comes from the sun.  So when you grow corn and turn it into ethanol, you are turning your field into a large solar collector and converting solar energy into stored energy.  But how efficient is it?

Tune in tomorrow to find out!