The commute carbon cost

I read an extremely urgent sounding news item today that actually did not contain any news.  It was the release of yet another report affirming the human cause of global warming.

It got me wondering about my commute.  Now that the weather is getting colder and biking is less and less of an option, I may find myself driving to work on a daily basis.  Audiobooks solve the traffic issue, can planting trees offset the emissions?

I estimate that my daily commute (around 12 miles each way) uses about a gallon of gasoline a day.  Gasoline is mostly carbon by mass so that’s approximately equal to 3 kg of carbon my commute releases into the atmosphere per day.  According to Trees for the Future, a tree will sequester approximately 23 kg of carbon per year, but unfortunately that’s only 0.09 kg per workday.

So to offset the extra carbon cost of my commute I will need to plant at least 33 trees.  They’ll take some time to mature before they can start soaking up that carbon dioxide at the above-assumed rate.  I’ll take suggestions for fast-growing varieties.

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Pinholes

The most hyped solar eclipse of the century passed over the U.S. mainland today. I viewed it through a homemade pinhole camera. Pinhole cameras, made of a hole, a length of empty space, and an imaging surface, have only two adjustable parameters: size of the hole, and distance between the hole and the surface, which is a focal length of sorts.  How does tuning these two parameters affect our image?

Image Size

The angle subtended by the sun is about 0.5 degrees in the sky.  It’s simple to see that the size of the image of the sun (L) does not depend on the diameter of the pinhole, but rather only on the distance f in the image below:

IMG_8081

Figure 1. Pinhole geometry

For a focal length of 1 m, L should be about 9 mm.

Angular Resolution

A more interesting question is how the image resolution might be affected by tuning these parameters.  It might seem that a smaller pinhole should create a sharper image (Figure 2), but there is a limit.

image2

Figure 2. Ray optics picture.  A larger aperture yields a blurrier image, since it allows rays from different parts of the object to be mapped onto the same spot on the image.

The smallest spot that can be formed on the imaging plane is ultimately limited by diffraction.  By making the aperture too small, diffraction can rapidly blur the resulting image.  That effect is illustrated below.

image1.JPG

Figure 3. Diffraction introduces uncertainty measurement of the ray’s initial direction.

The resolution of our system is determined by the more dominant of these two effects, so,

CodeCogsEqn (3)

which has the following dependence on D and f:

 

pinhole_diameter

Figure 4a.  Making the hole diameter too small is much more detrimental to image quality than making it too large

pinhole_focal

Figure 4b.  Resolution improves with focal length increase.

A contour map showing the resolution as a function of D and f gives a clearer picture:

pinhole_contour

Figure 5. Contour map of resolution as a function of D and f.  Blue is better angular discrimination.  Plotted as log(theta in degrees).

Based on the calculations above, the pinhole should have a diameter of around one millimeter, and the focal length should be made as large as allowable.

Eclipse Test

I placed 3 pinholes, sized approximately 0.8 mm, 0.2 mm, and 0.4 mm, in order, on an aluminum foil.  Then light sealed one of our moving boxes (f ~ 1 m) from our recent move.  Two hole cut-outs for the eyes allowed me to look inside (and take photos).

 

The different light levels for the full sun images can be seen in the right panel.

As the eclipse started I whipped out a slightly better camera to document its progress.

066B8621

Figure 6.  Mirror image of the sun beginning its eclipse.

Zoomed in series of images of the eclipse progress in Boston, MA.  The most coverage we had was around 65%.

 

 

There are several design improvements I would make on the next iteration.  First, I underestimated the importance of being able to get very close to the projected image.  I would need to place the eye holes closer or baffle in a different way so that the viewer can approach the imaging surface.  Relatedly, since pinhole cameras suffer from minimal tilt distortion I would tilt the focal plane so that the image can be viewed more head-on.

See you in 7 years.

 

About hysteria

I’ve tried to be positive, but it’s good to be realistic, too.

If you’re signed on to resist the agenda of this administration, you’re going to have to come to terms with being mis-represented, being mocked, being hated. Possibly forever with no vindication.

Because a resistance that actually succeeds in preventing an atrocity will never have evidence of its necessity or its success. Life will go on as usual. The nation will remain its unequal, imperfect self, hurtling towards some uncertain future. You may even have the privilege of being ridiculed in retrospect for your “hysteria”.

Yet that’s the nature of the thing. The window for resistance closes at a rapid rate as an atrocity becomes less speculative, more imminent. So, while we wait, afraid to be hysterical, afraid to be wrong, afraid to overreact, the ground beneath us is shifting.

The German author Emil Erich Kaestner once said, “the events of 1933 to 1945 had to have been fought no later than 1928. After that, it was too late. One cannot wait until the struggle for liberty becomes treason. One cannot wait for the snowball to become an avalanche. You must crush the snowball. No one can stop an avalanche…

What I’m trying to say is, don’t feel too bad. Resisting tyranny will always require paranoia and imagination. And it will always be the work of “hysterics”.

A conversation from Radiolab

http://www.radiolab.org/story/193037-turing-problem/

A: I think we’re just machines. I think we are just made of matter… For me, that doesn’t make me feel we’re any less special. I think, how, what a wonderful thing… How wonderful, that this process, and that these little collections of matter are able to produce Cezanne’s water colors and Bach’s preludes.

Q: But, could you, if I built you a computer, that could create equally beautiful watercolors, and equally beautiful musical compositions, would you feel happier or diminished?

A: I think, in a way you’re asking, if you see how the trick is done, does it then, vanish? Does it just become a trick? … I feel, the art I love, is always art that I don’t fully understand. There’s some mystery there, always. I don’t quite fathom it. Now so, if the computer is churning out a bunch of notes, and you know exactly the rules the computer is following, and there’s no mystery, how can that possibly be a great piece of music? And the answer is, we don’t know how the computer is going to do it, we don’t know how the machine is going to do it. And when the computer produces music that is as lovely as the music that you and I love, I believe it will still be unfathomable.

Spring

The rain lifts
but a wet green clings
to all things. The air
shimmers like a full glass. This
was as much water as the earth could hold.
This was what
it takes to hatch life–
to squeeze new buds
through hide-black bark grown thick
and coarse from wear.

Spring in the city. Here,
where we read
by the light of one
another’s window,

where we live in relative quiet
our ancestors must envy, lulled
by the gentle tilt
and sway of our days,
each as ordinary as cloth,
as dull as dust.

We will meet when
the water recedes. Where
we will meet the traffic sounds
in the distance and white petals fly
and climb
to unexpected heights, taken
by the wind in circles
wider and wider.

(There are many such spots
in the city, to imagine
how it must have been
at the toppling of the towers, at
the setting of the seas…)

Soon enough,
we too will be blown out in the wind.
So, if we are not happy, at least
we are fearless to expire.
Even as the soggy land falls
back into the belly of the sea,
we look for footing.

 


I wrote a poem about rain.  But I do wish it would stop raining.