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04 July 2009 @ 07:19 pm

The following is in conjunction with "The Mirage of a Growing Fuel Supply"by Evar D. Nering, which appearedas an op-ed in the NY Times in June 2001, illustrating consumption of a non renewable resource when used at a rate that grows as a percentage of itself each year.

Below is a derivation of the formulas and how he arrived at his numbers.
If a quantity is consumed by some rate of itself per unit time, dt, the consumption  dy used equals

dy=kydt, where k= rate of consumption

dy/y=kdt integrating both sides of the equation gives

lny=kt + c or

y=ce^kt at t=0 and y=yo ,c=yo


if V=total quantity consumed from t=0 to t=t1

V=integral from t1 to t0 of yoe^ktdt,

V=yo(e^kt-1)/k ,solving for t

e^kt=Vk/yo +1

kt=ln(kV/yo +1)

t=ln(kV/yo +1)/k

then for

(1) k=0.05, V/yo =`100 years, t=ln(0.05x100 +1)/0.05, t=ln6/.05=~36 yrs.

(2) k=0.05, V/yo =1000 " , t-ln(0.05x1000+1)/0.05, t-ln 51/0.05=~79 yrs

(3) k=0.05, V/yo=10,000 " , t=ln(0.05x10,000 +1)/0.05, t=ln501/0.05 = ~124 years

29 September 2008 @ 01:55 pm

If the average mileage of cars and SUVs in the US is 22 miles/gallon and the average car travels 12,000 miles/year, then the average vehicle uses 12,000/22~ 545 gallons/year. If the US fleet consists of about 180 million cars and SUVs,then, 180 million x545=~98,180 million gallons per year or (dividing by 365 and 42gals/barrel) gives us 6.4 millionbarrels per day/(mbd) used by cars and SUVs.

.   If we were to double our mileage to 44 mpg then, 12000/(44)x180/(365x42)=3.2 million barrels/day consumed. The savings on imports amounts to 3.2 mbd. If we're currently importing about 12 million barrels per day, then the percentage is3.2/12 ~ 27 %. Well worth achieving.

   If we could raise our average to 50 mpg then the average use per vehicle would be 12,000/50~ 240 gallons/year.then following the same procedure we'd consume 240x 180 million /(365x42)=~2.8 million barrels per day.The difference of how much lesss oil we'd have to import is 3.6 millions barrels per day. In this case we'd cut our imports by 3.6/12 =.3 or 30 percent.This would give us a good deal of  .independence from the Persian Gulf Emirates.

The above assumes that a gallon of crude oil will produce about 1 gallon of gas.

28 July 2008 @ 06:24 pm

From time to time someone mentions that there is a herd mentality regarding anthropogenic climate change.Perhaps this is due to a lack of understanding of why many of us are proponents of anthropogenic global warming. It is based on observed data as well as first principles of physics, not by blindly following any kind of herd.

There has been a fairly steep rise in average temperature in the last 3 to 4 decades. The heat content of the ocean's upper layers has increased over this same time period. Mountain glaciers, nearly everywhere have been shrinking at increasing rates,and arctic sea ice is melting, also at an accelerating pace. Greenland's ice cap is doing the same. The diurnal temperature range is decreasing due to a quicker increase in night time over day time temperatures. Hurricane intensity is increasing( see Flora and fauna have been migrating to higher latitudes and to higher elevations. The average temperature of the globe has increased about 0.7C over the last century or so. These conditions are based on observations.

A well established principle of physics states that climate results in a balance between incoming solar energy and the amountof heat that planet radiates away to space. An atmosphere can absorb some of that outgoing energy, altering the energy balance which would keep that planet warmer than it would otherwise be- the greenhouse effect. These gases, primarily H2Oand CO2 makes Earth about 33C warmer than if these gases weren't present. Changes in the amounts of these gases will change this number, and carefully measured values of CO2 show that this gas has increased significantly since the dawnof the industrial age.

For the last 250 years or so we've been burning fossil fuels which releases carbon into the atmosphere as carbon dioxide,CO2. About half of that carbon remains in the atmosphere resulting in an increase of about 115 ppmv of C02 since thestart of the industrial revolution(from 270 to 385). From an examination of ice core data, this number is higher than it hasbeen in at least the last half million years.Deforestation and land use practices also affect climate. These factors have tobe taken into account to explain the recent changes in climate, described above.

09 January 2008 @ 04:44 pm

    An article in yesterday's New York Times by Andrew Revkin dealing with rise in sea level from melting glaciers  cites Dr. Eric Rignot of NASA as saying that unabated global warming could result in 3 feet of sea level rise from melting ice on Greenland and another 3 feet from Antarctica and about 18 inches from the melting of Alpine glaciers. He quotes Dr. Rignot as stating: " it is too early to reassure that all will stabilize and similarly there is no way to predict a catastrophic collapse," ....." But things are definitely far more serious than anyone would have thought five years ago." (Emphasis mine). 

   There's an old expression-"Stop the world, I want to get off." Well just in case the worst does happen, we may have think of having to go elsewhere(getting off in a sense). Where? I don't know, but here's the calculation on what  upward speed we will need to get off. 
  We're going to determine the velocity of a particle projected outward  in a radial direction from the earth and acted on by only one force, that of gravity.

  According to Newton's theory of gravitation , the acceleration of the particle will be inversely proportional to the square of the distance of the particle from the center of the earth. 
   Let  r be that distance and R be equal to the earth's radius, t is time, a represents acceleration and k is    the proportionality constant  in Newton's law. 
  Then  a = dv/dt=k/r^2  
  Since the acceleration is negative because  the velocity is decreasing as it travels upward, then k is   negative. When r=R  and a =-g,   then g=-k/R^2. Substituting for k above, gives a= -gR^2/r^2.
  Since a =dv/dt and v=dr/dt then:
  a= dr/dt(dv/dr) =vdv/dr so that our diff equation  is : vdv/dr= -gR^2 / r^2
   The solution is v^2= 2gR^2 /r +c 
  When v=v0 and r=R then c = vo^2- 2gR  so that a particle projected radially outward will go with a velocity 
  v^2=2gR^/r +v0^2- 2gR. 
    In order to escape from the earth the quantity v0^2-2gR > 0 (must be equal to or greater than zero).
   So then the vo=the square root of 2gR  is the escape velocity required . R=3,960 miles(approx.)  and 
   g= 6.09x10^-3 miles/second^2,   so that v0 =6.95 miles per second. Frictional air resistance in the lower atmosphere may not be negligble so that a slightly higher value may be required.              

03 August 2007 @ 04:46 pm
   To continue where I left off a few days ago. The 1400 watts per square meter  we receive from the Sun at the top of our atmosphere translates to about 245 watts per square meter at the surface of the Earth when albedo and the Earth's rotatation is taken into account.. This assumes a mean distance from the Sun of 150 million kilometers. If the Earth were 153 million kilometers from the Sun we would reduce the 245 to 235 watts per square meter! Since a doubling of anthropogenic carbon dioxide in the atmosphere  increases the energy rate by about 4.5 watts per square meter, the 10 watts/meter^2 would erase the effects of quadrupling the CO2!
    In other words to offset the projected of effects of global warming by quadrupling the atmospheric  CO2 we would merely have to move the Earth about 3 million kilometers further from the Sun. (Don't try this at home) I say 'merely' but there are downsides to this solution. For one thing we could overshoot and one of the outcomes could be that we'd become a satellite of Jupiter! Wouldn't that be a hoot!? There would also be effects from the force caused by the initial acceleration in accord with Newton's second law. Who knows what these effects would be. Earthquakes? Seismic sea waves a hundred meters high? Perhaps this isn't such a good idea after all. We'd probably do well to doing things like switching to alternative fuels.
28 July 2007 @ 10:13 am

    I believe I've figured out what we must do. Here it is the middle of the 21st century and our home planet is getting warmer and warmer. There's barely any ice left on Earth, except for central Antarctica. The east coast of the U.S. is just offshore of Pittsburgh, where summer daytime temperatures compete with what used to be average for Texas or Arizona back in the year 2007.

What's needed is a solution, which I'll get to later on, to undo the warming or we are undone as a civilization. The main problem is that the carbon dioxide levels are nearly at 600 parts per million by volume, more than twice the concentration than existed in the beginning of the Industrial Revolution. This doubling means that the rate of heat energy coming to the Earth's surface as a result of the enhanced Greenhouse Effect has increased by 4.5 watts per square meter. We must somehow undo this by whatever means we have available. I've done some prelimination calculations and find that we are receiving a total solar intensity of heat rate in the upper atmosphere of about 1400 watts per square meter. ( To be continued)