On Mar 21, 2008, at 4:40 PM, Nick Palmer wrote:
Could Vorts look over the paragraph below and give me their opinion
on it (also please check the maths). It is part of an article I am
writing for our newspaper on sustainability.
<< Perhaps people do not realise how little environmental
space we all share because there is a rather strange belief around
which often comes out in anti-Green propaganda articles,
particularly in relation to global warming, where the protagonists
try to lead us to believe that we cannot possibly affect the
environment of Earth because we’re so puny and the earth is so
large. These people must be mathematically illiterate. In the late
1960’s people raised concerns about the growing population and
scoffers at the time claimed that the entire world’s population
could squeeze onto the Isle of Wight (although this assumes just
over one square foot each!), thus making the world then appear a
pretty roomy place. I did the complementary calculation and
discovered that if the global population then (3.6 billion) was
evenly distributed over of the land surface of earth, then each
person would only have an area of land 220 yards square as their
personal environmental space! Obviously some of the land would be
hostile desert, ice fields, mountains, rainforest etc. The world
suddenly looked rather cramped. I recently did similar
calculations again, using the current world population figure of
6.6 billion, and our current personal environmental land space is
now down to 150 metres square (164 yards square) per person. I
then went on to calculate what size our personal spaceship is today
within which we metaphorically have to live our lives, use energy,
manufacture goods, dispose of waste, extract minerals, grow food,
catch fish and dissipate pollution, pesticides etc within.
Surprisingly, our personal spaceship works out to be a globe only
about 1.18 kilometres in diameter within which we have a piece of
Earth’s surface about 277 metres square (of which 70% would be
ocean). Perhaps this helps to make it clear why the total number of
people multiplied by their individual impacts on the planet has now
brought us to the point where we can put up a “House full” notice
on planet Earth. >>
The figures etc I used are easily findable.
Radius of Earth = 3960 miles
Surface area of sphere = 4pi x r squared
Proportions of land compared to ocean 30%/70%
Column of atmosphere above us, assuming pressure of one atmosphere
to the top, 10.6km. (worked out using sea level pressure and density)
Volume of personal spaceship's atmosphere = 10,600m x 277 x 277 cu
metre
Radius of personal spaceship = cube root of (Volume divided by pi x
3/4)
I assumed that the spaceship should have constant atmospheric
pressure throughout (as it would in space) to make things simpler
to visualise because any gaseous pollutant introduced within the
body of gas would reach roughly the same relative concentration to
other gas molecules whatever the pressure; that is to say that one
gallons worth of fossil fuel fumes would expand to a much greater
volume high in Earth's atmosphere but the relative concentration
would stay approximately the same.
Nick Palmer
Using an earth radius of 6371 km.
http://en.wikipedia.org/wiki/Earth
The density of air at the earth's surface is 1.2 kg/m^3, The mean
mass of the atmosphere is 5.1480×10^18 kg.
http://en.wikipedia.org/wiki/Earth's_atmosphere
The surface area is 4 Pi (6371 km)^2 = 5.1x10^14 m^2. The volume of
the earth's atmosphere at average humidity and temperature conditions
is (5.15x10^18 kg)/(1.2 kg/m^3) = 4.3x10^18 m^3. The per capita
volume for 6.6 billion people is then (4.3x10^18 m^3)/(6.6x10^9) =
6.5x10^8 m^3. The per capita surface area for 6.6 billion people is
(5.1x10^14 m^2)/(6.6x10^9) = 77272 m^3, or 278 meters square. If
each person gets a 77272 m^2 room, then the ceiling height is
(6.5x10^8 m^3)/(77272 m^2) = 8411 m, or about 8.4 km. so that's a
long way between floors.
The volume V of a sphere to hold all that gas is V = 4/3 Pi r^3, so r
= ((3V)/(4 Pi))^(1/3) = (3(4.3x10^18 m^3)/(4 Pi))^(1/3) = 1x10^6 m,
or about 1000 km.
As always, you may want to check my arithmetic.
Horace Heffner
http://www.mtaonline.net/~hheffner/
