i think that i shall never see / a carbon offset as lovely as a tree

Cpp_avatar I overhead an exasperated parent the other day:  “The kid just won’t stop asking ‘why’ all the time.  Everything I say, she challenges.  She’s driving me absolutely nuts.”

We need more kids like that.

I know, easy for me to say since I’m childless by choice, but I really do believe that the biggest danger we face as a society is a populace that doesn’t want to think for themselves.  I am more than happy to have students challenge me about the material I teach.  In reality, though, they spend a lot more time challenging me on my attendance policy, my lack of understanding that they missed class due to a hangover, my grading policy, and my refusal to allow ‘do-overs’ for tests that didn’t produce the desired scores.  Most disppointingly, so many test answers are phrases regurgitated directly back from my notes with no evidence that the writer spent even a few seconds considering what those words meant and whether they were right.

While professors hate this trend, marketers but be thrilled.  Someone tried to argue the other day that the Tesla Model-S electric car was actually cheaper than a luxury gasoline sedan.  He told me that the New York Times said that the $57,400 list-price Tesla Model-S was actually only $35,000 "when you accounted for tax credits and gas savings". 

Sure enough, there was Elon Musk saying that the Tesla sedan would cost $57,400 list price, $49,900 after tax credits, and $35,000 “after factoring in gas savings”.   Anyone have a bell go off there?  A 'one of these things is not like the others' moment?

You can’t directly compare the first two items with the last.  There is a difference between one-time costs (purchase price and tax credits) and the more-nebulous issue of "gasoline saved" because the latter depends on how much you drive.  It will vary from person to person and it's money you get back, not money you don't have to put out in the first place. 

Probing further, I found an actual quote on a GM site about the Chevy Volt, which quotes Musk as saying.

“The ownership cost of Model S, if you were to lease and then account for the much lower cost of electricity vs. gasoline at a likely future cost of $4 per gallon, is similar to a gasoline car with a sticker price of about $35,000. That’s why we’re positive this car will be the preferred choice of savvy consumers.” 

Arg.  Now we’ve got leasing thrown in and I have no idea how they calculated the cost of the electricity  used to charge the car.  Inquiring minds want to know.  Or, at least, they should.

Goodyear does a pretty nice job in advertisements for low rolling resistance tires.  They tells us that we’d save 2600 miles worth of gas over the life of the tires.   An asterisked statement tells us that this estimate includes a lifetime of 65,000 miles and a 4% increase in fuel efficiency.  They even provide a calculator for you to input your car's mileage so you can see how much money you’d save.

During interviews for my Physics of NASCAR book, I interviewed a Todd Meredith, a manager at Joe Gibbs Racing.  I always ask whether a race shop has any employees with a physics background, since most are mechanical or aerodynamics engineers.  Todd thought for a moment and said,

“Yeah, I think we do… but I bet he doesn’t use anything you taught him.”

“I bet he does,” I shot back, “because we taught him how to think.”

That started a really productive and interesting conversation about the importance of science and math and how they are taught. In the end, racing is real-time advanced problem solving, and all the skills you learn as a scientist, engineer or mathematician are exactly the skills you need to be part of a race team.

Fundamentally, science and math are about learning how to evaluate data to ensure it’s valid, synthesizing multiple data sources, critically analyzing that data and coming to conclusions. We need these skills more now than at any other time in history.  Climate change, energy, manned vs. unmanned space programs, oil well leaks…  even if you don’t understand the details of the science, you HAVE to be able to understand if you’re getting the truth or being sold a load of goods.

It’s hard enough for scientists to find ‘The Truth”.  There are significant disagreements on directions for action in many areas (climate change, transportation, etc.) because we simply don’t have enough data to make unequivocal conclusions.  Although there have been some issues with advocacy getting in the way of science, that’s nothing compared to the number of people who are purposely twisting science to their own goals.  If Shakespeare were alive today, I suspect he would have chosen "public relations persons" rather than lawyers as his occupational target of choice.

The honorable people in marketing and public relations bring to light the most positive accomplishments of their company.  There are those who are less honorable.  How much "news" is actually a minimal re-write of a press release?  Some science "news" sites are simply places for universities and companies to post their news releases, and some science journalism is little more than a thin re-write of said news release.  Science is not the only place this happens.

I heard a NASCAR broadcaster make the following claim: "NASCAR offsets 100% of the carbon emissions from this race via their tree-planting program."  Anytime someone says "100%" or "always" or "without exception", my ears perk up.

OK, NASCAR has been (and is) doing a lot of good things to be environmentally responsible.  They were recycling used oil before it was cool, they are initiating recycling programs at tracks, even getting teams to minimize how much they run generators during race weekends.  All good things, but not very exciting.  Newspapers don't want articles about recycling oil.

But tree planting… beautiful PR idea.  Get your biggest stars out to dig the holes, put the trees at a local school or park.  Bingo.  So how many trees do we have to plant?

Some brilliant NASCAR PR person did major damage to the cause of logic and educating the public by deciding that they would plant ten trees for every “green” flag during a race.  Green flags wave at the start of the race, and after every caution, so the number of green flags depends on the number of accidents and amount of debris on the track. 

This is just wrong on so many, many levels, and it's not like this is difficult science.

Combusting one gallon of gasoline produces 19.4 pounds of carbon dioxide.  One gallon of gasoline weighs about 7 lbs – the additional mass making up the carbon dioxide comes from the oxygen that combines with the gasoline during combustion.  Two octane molecules combine with 25 oxygen molecules, which explains how the weight of carbon dioxide is greater than the weight of the fuel. 

But the important point here is that the amount of carbon dioxide emitted is directly proportional to the number of gallons of gasoline combusted.  Not only does this have absolutely NOTHING to do with how many green flags wave during a race, it’s a number we can calculate with pretty reasonable precision.

Forty-three cars run 500 miles, each getting about 4 miles per gallon.  I am overestimating the amount of fuel used by just a little:  the cars get about double the gas mileage during cautions and some cars don’t run the full race.  I’m calculating the upper bound. It wouldn't be hard to use the data on exactly how many laps were run by each car, but I'm not the one claiming I'm planting enough trees to offset the emissions, so I'm making an estimate.  When you do the calculation, it's about 5,375 gallons of gas in a 500-mile race.

GallonsGasI know – you’re horrified at this tremendous waste of gas.  Get over it: In 2009, the Department of Energy says the US consumed 137.93 billion gallons of gasoline. That means this country uses 4,373 gallons of gasoline every second. I guarantee you I could easily find enough U.S. NASCAR fans who would volunteer to use less gasoline in their everyday lives to compensate. Compare a weekend of NASCAR (including the media coverage and fans getting to the track) with a weekend of the NFL. You can make a better argument for saving fuel and emissions by eliminating a weekend of NFL football than you can a weekend of NASCAR.

Nonetheless, my hypothetical NASCAR race still uses 5,375 gallons of gasoline, which means that 104,275 pounds of carbon dioxide (about 52 tons) are released into the atmosphere.

One of the first things I remember learning about science is that people breathe in oxygen and breathe out carbon dioxide, while plants “breathe in” carbon dioxide and emit oxygen.  Photosynthesis combines water, carbon dioxide and energy from the sun to produce sugar and oxygen gas:


Six carbon dioxide molecules and six water molecules combine to produce one sugar molecule (the C6H12O6) and six molecules of oxygen.  Plants covert the sugar into organic matter like stems, leaves and stalks.  

The problem with plants is that they lose their leaves (and, if they live in my house, they die).  The real masters at storing carbon are trees, because trees convert sugars into cellulose — long chains of the repeating unit C6H10O5.  As long as the tree is growing, it’s sucking up carbon dioxide.   Since each of us generates about 2.3 tons of CO2 each year, we should all be doing out part to encourage trees to grow.

Now for the tricky question:  How much carbon dixoide does a tree absorb?  Turns out that's not as easy a question to answer as I thought.  You can find numbers ranging anywhere from 10-70 lbs of carbon dixoide per tree per year.

Let’s analyze this.  Since carbon dixoide is mostly stored as wood, the amount and type of wood are going to be important.  In other words, when it comes to trees and carbon sequestration, size matters.

Assume a cylindrical tree.  The volume of the tree goes like the diameter of the tree squared times the height.  Compare two trees of the same species the same height, but diameters that differ by a factor of two.  The one with the larger diameter stores four times as much carbon dioxide (pi r squared!).  The difference in storage is even larger, of course, because trees (unlike people) continue to grow upward, as well as getting larger around the trunk as they age.

Trees with denser wood store more carbon dioxide than trees with less dense wood.  Next time you’re at the home improvement store, compare trim made from pine with that made from oak or cherry.  I’ve summarized the mean densities of a couple of different species of trees on the graph below, which shows the height of the tree on the vertical and the type of tree on the horizontal axis.  Sorry about the labels being so small.  From left to right, they are: balsa, red pin, red oak, cherry, ebony and lignum vitae.  The densities are given in kg/cubic meter and range from 160 to almost 1400.  Red pine has a density of 370 – 660 kg/m3, whereas ebony (a hardwood) has a density of 960 – 1120 kg/m3.  The champ in terms of tree density is a tree called Lignum Vitae, which has a density of 1280 – 1370 kg/m3.



I noted that the larger the tree is, the more carbon it has stored.  So you might think big trees are the best to plant.  But what's really important is how fast the tree is growing – how fast it can convert carbon dioxide into wood.  Big means that the tree has stored a lot of carbon.  Fast growing means that the tree is storing a lot of carbon 

A tree grows slowly in the early years (while it's putting down roots), then has a period of more rapid growth, and finally tapers off as it approaches its maximum height, as I’ve diagrammed below.  The region of maximum growth is at the steepest parth of the curve, so you want to plant trees that are near the maximum in the derivative of their height vs. time curve.  Unfortunately, most nurseries do not put this data on the little tags that hang on the trees when you go to buy them.  Forestry types tell me that Southern Pine may reach its maximum growth period in 20-28 years, while Douglas Firs on the Pacific Coast require 60TreeGrowthRates years.  Things are a little more laid back on the Left Coast.

Speaking of laid back, consider also that tropical trees account for 95% of all tree-based carbon dioxide sequestration on Earth.  A tree without leaves isn’t doing much photosynthesis, which means it’s not removing carbon dixoide from the atmosphere.  Tropical trees work 12 months of the year, while boreal trees only work 3-6 months of the year.  Tropical trees are mostly hardwoods and grow more quickly than their cold-weather relations, so there are a lot of people who advocate that, if you're going to support tree planting, you should send money to oragnizations that are trying to re-plant tropical rain forests because those trees are more likely to have a larger impact than the pine trees you plant at a local park in New York.

There are some ways of estimating how much carbon dioxide a tree will take in each year, like determining the mass of the tree based on its dimensions.  One is a really great exercise for middle or high school students.  They find that:

  • A 10 year old Grevillea robusta (the southern silky oak, an evergreen Australian tree) that is 45 feet tall and 6 inches in diameter would sequester about 64 lbs of carbon dioxide per year.
  • A newly planted Acacia angustissima (native to Central America and the US) at 2.5 yrs, 15 ft tall and 3” in diameter would take up about 21.5 lbs of carbon dioxide per year.
  • Calliandra calothyrsus (powder puff tree, Mexico, Centra America) that is 10 years old, 15 feet tall and 8” in diameter would remove about 65 lbs of CO2 per year.

In general, trees planted in the US have a difficult time reaching the numbers tropical trees can achieve.  Most people, noting that environment, rainfall and other conditions matter, will use an estimate that a tropical tree can absorb an average of 50 lbs of carbon dioxide per year.   "Tropical" usually means within 23 degrees North or South of the Equator, but let's count Florida as "tropical".

Let’s be generous and use the 50 lbs of carbon dioxide per tree per year number, which is probably 1.5 to 6 times larger than reality.  To offset the 104,275 lbs of carbon dixoide from the NASCAR race, you would need 2,085.5 year-trees.  "Year-trees" means that the product of the number of trees times the years the trees are sequestering carbon needs to equal two thousand and eighty five.  You could plant 2,085 trees and they will compensate for the race in one year.  Or you could plant a thousand trees and compensate in just over two years.

Last year’s Daytona 500 had nine cautions, so including the green flag that started the race, there would have been 10 green flags and NASCAR planted 100 trees.  The calculations above show that those 100 trees will offset the carbon emissions from the race in just under 21 years.  And I'm being really generous with giving each tree credit for 50 lbs of carbon dixoide per year.  If that number is 25 lbs per tree, we're talking more than 40 years before all the carbon from those five or six hours last February have really been accounted for.  (And yes, I do know that the race went 520 miles due to multiple green-white-checkers and I didn’t add in those extra 20 miles, which is another 215 pounds of carbon dioxide, and ignoring that probably accounts for the laps under caution and the cars that dropped out before the race was over.)

That estimate doesn't include the carbon emissions needed to take care of the trees for that long:  fertilizers, vehicles, replanting trees that die, etc.  

 In 2009, Petaluma Junior High School received 30 trees from NASCAR and Infineon Raceway to offset the carbon emissions from the race in Sonoma.  Sonoma is a road race, so it is shorter (224 miles) and we’re “only” talking about 2,408 lbs of carbon dixoide.  The kids from that junior high school are going to have their own kids in junior high school before the carbon from that race is offset.

Offsetting carbon emissions from planting trees is not the panacea it has been advertised to be.  One website calculates that, in order for the Earth to become carbon neutral, we would have to reforest a land area approximately equal to Spain every year and maintain that land in perpetuity.

The small impact NASCAR's trees will have on the environment is at least good; however, their decision to pursue – and publicize – a non-scientific approach to the problem is grievously wrong.  I'm offended  NASCAR thinks I'm stupid enough to fall for this. 

I'm also a wee bit irritated at some members of the "NASCAR media" who are willing to parrot the 'facts' they are handed without question.  I don't expect them to be experts, or even have time to call up a scientist to ask whether it's accurate. 

The fact of the matter is that you get credit for sequestering carbon as it is sequestered, just like you get credit for paying down your mortgage as you make the payments.  You don’t own the house by taking out a mortgage and you don’t offset your carbon emissions the minute the trees are in the ground.

As I tell my students over and over again:  If you don't understand something, the last thing you should do is repeat it.

Neat trivia I learned while researching, but couldn't slip into the blog:  Forestry professionals use the abbreviation "dbh" when describing trees.  dbh means "diameter at breast height".  Breast height is defined to be 1.4 meter.  There are apparently very strict physical requirements for being a forrestry professional.


5 thoughts on “i think that i shall never see / a carbon offset as lovely as a tree”

  1. Is there any value at all to planting trees? Or carbon offsetting?
    The above figures indicate we’re doomed & shouldn’t even try. Don’t even start kids thinking about the environment. They might encounter bad data, for starters. If they took action, they’d be a part of “the big lie”.
    When you destroy a position, I often wonder if there’s a better alternative.

  2. diandra@trivalent-productions.com

    RA: Planting trees can be a positive thing if you plant the right trees in the right places, but just planting trees isn’t going to solve the problem by itself. Planting trees isn’t bad. My objection is that stunts like give people the wrong idea of the impact their actions have. The first step is knowledge. Then you can make a choice as to whether you think you should change your behavior. Of the ‘reduce, reuse, recycle’, we’ve focused much more on the latter than the former.

  3. Agree with your outlook regarding learning how to think, especially thinking critically. Honor is where you find it and no group or association has a lock on it. One of the greatest pleasures of teaching is finding and helping create a resonance in thinking minds, and then of course one of the greatest downers is in not finding it at all.
    Your brief analysis is a good example of how to react to bald faced statements and claims that are as ridiculous on their face as they are common. However, it can also serve as a good example of how impossible it is for science to claim it can model complex natural events. For instance, tropical forests are not all active throughout the year as those who live in such areas know. Many ‘tropical’ forests are deciduous and their leaves turn all the lovely colors of fall we see in our temperate climes and drift to the ground every year. Currently I am somewhere around the 20th latitude, lots of the trees are in fall colors and mounds of leaves cover the yard and walk ways. Many that are consistently green are not really trees as we think of them but rather are rhizomes, the best known being the beautiful and useful banana ‘trees’, which do not contain any hard cellulose based ‘wood’ as we know it, and which unceasingly and vigorously sprout anew from a parent rhizome in communal bliss.
    Which brings us to another point which is that plants convert a lot of CO2 into flowers and fruit. Wood is about individual survival, flowers and fruit are about the continuation of the species and the host of symbiotic relationships that make up a system too complex for mortal man to understand except as art and love with some mysticism thrown in for good measure.

  4. “I really do believe that the biggest danger we face as a society is a populace that doesn’t want to think for themselves”
    (PS: But there’s hope!)

  5. Oh, so helping buy a plot of land in the rainforest when I was in Kids for Saving the Earth was actually the best plan! Good to know.

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