Re: [Vo]:Environmental space

[Horace Heffner]

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/