Green House Gases and Automobiles

Written 2002

Formatted 2009


Recognizing mathematical thinking in a common news worthy issue

We have all heard the claim that green house gases generated by human activity, such as driving automobiles, are causing global warming. Some people argue against this claim. Activists have lobbied congress to regulate the automobile industry to create more efficient cars. Is this a wise approach? Is it the best approach? A little simple mathematical thinking can take us a long way in evaluating this problem. Below we will examine a few core elements of this discussion.



Part 1: Systems - Distinguishing between balance and imbalance

A system, such as our ecosystem, will be sustainable if it is balanced. Here we ask do we have evidence that human activity has made the atmosphere of our ecosystem unbalanced?

Systems: Source vs. Sink


  • Source: anything that produces (greenhouse gases or CO2 in this discussion). "Automobile emissions source CO2"
  • Sink: anything that removes or extracts. "Photosynthesis sinks CO2 from the atmosphere."
  • System: things that are intrinsically related to each other through feedback.
  • Feedback: the output of one side becomes the input of the other. "Human activity uses O2 and produces CO2. Plant life will feedback O2 to humans by inputting our CO2 and producing O2 as output.
For a system to be stable, for every source there must be a sink. For every ton of CO2 produced there must be a ton extracted. We know that human activity produces CO2. We know that CO2 can be extracted biologically with photosynthesis. We have found some evidence that CO2 can be extracted geologically. But in the end, for the ecosystem to remain stable for every ton of CO2 produced, by any source, a ton must be extracted. Otherwise the system will be unstable; CO2 build up will occur.

The concept is simple:

Balanced System
Source = Sink
Source = Sink + Excess
For any system to be stable: the rate of production (sourcing) must be equal to the rate of extraction (sinking).

Systems: More roads <--> More cars

Systems thinking can be used to look at the feedback that exists within human society. As more cars are produced, more roads are built. Building more roads makes room for more cars. This is a system that has "positive feedback."
Unfortunately, not only does every car produce green house gases, every road built eliminates some of the space where photosynthesis would be extracting CO2. The creation of more sources of gas results in the destruction of the potential biological sinks.

Conclusions: For the atmosphere to be stable, the CO2 must be extracted from the atmosphere at the same rate it is being produced. The very human systems that produce CO2, reduce nature's ability to extract CO2.

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Part 2: Recognizing the factors in greenhouse gas production (considering only transportation for this evaluation)

Let us start by thinking about the factors that make up the problem. A person does not need to be a mathematical genius to create a list of factors. Obvious factors include:

  1. the efficiency of the engines
  2. the engines' pollution control equipment
  3. the number of cars
  4. the number of drivers
  5. the number of miles each car is driven
In the end, we will claim that we can approximate greenhouse gases coming from cars as:
  • g = the greenhouse gas produced each year
  • v = the vehicles
  • Sigma = means to add up each vehicle
  • c = the conversion rate of gasoline to CO2
  • d = the distance each car is driven
  • I = the inefficiency of each engine
  • g = greenhouse gas produced each year
  • v = the total vehicles
  • c = the conversion rate of gasoline to CO2
  • <d> = the average distance each car is driven
  • <I> = the average inefficiency of each engine
We will show that considering each factor, and the relationship between the factors, will change our emphases when we propose solutions to the problem.


Engine Efficiency and Pollution Control Devices
The activists have focused strongly on these two considerations. Pollution comes from cars, cars come from corporations. Corporations are easy to regulate. But what do we conclude when we consider the vehicle's efficiency and pollution control devices.
Each car, in fact, any burning, emits various gases including carbon dioxide, oxides of nitrogen, hydrocarbons, etc. Most of the gases are greenhouse gases, and many of them decompose into carbon dioxide. Since all fuel burned turns into greenhouse gases, and most of the gases decompose into carbon dioxide, a rough estimate of green house gas production then becomes the total amount of fuel burned.
So, the activists are right, increasing efficiency decreases green house gases. But did they over look anything? Remember, vehicles do not always carry just one passenger. More passengers means more passenger miles per gallon. So a train carrying 200 passengers will be more efficient than a bus carrying 40, a van carrying 4 or a car carrying 1.

passengers using the same amount of fuel
So the first thing to recognize is: Everything that makes the driving less efficient (passenger miles / gallon) contributes to greenhouse gases. This means not only less efficient engines but also less efficient behaviors.

Things known to reduce engine efficiency:

  • torque
  • pollution control devices
  • car weight

Things known to reduce efficient behaviors

  • riding alone
  • traffic jams
Conclusions: Increasing efficiency will reduce greenhouse gases. The efficiency increase of using public transportation is far greater than the efficiency gain of gas mileage improvements.


Miles each car is driven

Automobile efficiency has increased significantly since 1970, but fuel consumption, and gas emissions have increased. The distance Americans drive each day increased significantly during that time.
The significant increase in driving has resulted largely from suburbanization and zoning laws. Americans have moved to less efficient lifestyles in the suburbs. They have passed zoning laws stating that places of work and shopping must not be built in residential neighborhoods. This means suburbanites must drive to take care of any and every need.

The environmental implications of this are severe. Suburban zoning laws and life styles have offset all of the efficiency gains of the engines in terms of total environmental impacts. Suburbanization has contributed more to green house gases than underefficient engines. Everything that is causing us to drive more is contributing to greenhouse gases.

Conclusions: Suburbanization and zoning laws are major causes of greenhouse gas emission.

The Number of Vehicles and Drivers

It doesn't take much to see that for every person driving, there is more fuel being consumed and more gases being emitted. So for everyone who needs to drive, or chooses to drive, more greenhouse gases will be produced.

The obvious implication is that an increasing population results in increasing greenhouse emissions. Similarly, increased dependency on technology results in increased greenhouse gases, even while engines become more efficient. If the number of drivers doubles, the fuel efficiency must also double, just to keep the emissions at the same level.

Conclusions: The rising population and dependency on technology are major factors in greenhouse gases.

Part 2 Conclusion: Indirect factors, such as population increase and suburbanization, can have a greater impact than direct factors, such as fuel efficiency.

Generalization: Environmental Impact = standard of living * Inefficiency * population

Problem solving ideally ends with recognizing how the elements of one problem, and thinking skills used to evaluate that problem, can be generalized to other problems. To generalize from this problem we recognize that each human alive has an impact on the environment, and the resources each human uses to increase his standard of living increase that impact. The population explosion is a factor in every environmental problem that humans create. Increasing the population results in increasing the problems. The desire to produce a better life, and inefficient methods of achieving that goal are also factors.



Part 3: Buffering

Buffering is an element of chemistry and physics where a system remains stable even though it is being pressured to change. Buffering is an essential element of the chemistry of life. The best known example of buffering is the ability of blood to keep its pH stable even when the CO2 concentration in the blood is being changed by external forces. The Gaia hypothesis is based on evidence that our planet has buffering systems that are analogous to the buffering systems found in living things.  

One of these buffering systems would be the ability of the planet to buffer the CO2 in the atmosphere, and to buffer climate changes that might result from changing CO2 concentrations.

The problem with buffering systems is that they have limits. Consequently, a buffering system will mask (cover up) the change that is occurring until the system is pushed beyond its limit. By the time the change becomes evident it is too late, the system is already out of control. If human blood is forced beyond the limits of its natural buffers, unconsciousness or death may occur.

Conclusion: If we wait until climate change and CO2 build up are clearly observable, we have waited too long.

Part 4: Record Temperatures

Some people claim that we still have many days where record cold temperatures are set. How could that happen if global warming is occurring?

Record temperatures are an element of statistics. So some basic statistics is needed to examine how many days of record temperature should we expect to have. Humans have been keeping temperature records, in some areas, for little over 100 years. The first year records were kept, every day had a record low and a record high for that day. Every month had a record low and high for that month and the year itself was both a record low and a record high. The next year we would expect that about half of the records would be broken. The year after that about a third of the records would be broken.

One hundred years later, we would still expect about 4 days (approx.: 365/100) to set a record high and another 4 to set a record low. We would expect a month to be a record hot or cold month only about once a year (12 months / 100 years of record keeping.) We would only expect a 1% chance of having a year that was a record hot, and equal chances of a record cold year. The rate at which records are being set is higher than the expected rate. This suggests that some type of change is occurring.

There is evidence that day time high temperatures are staying about the same as they had been, but night time lows are gradually rising. If this is the case, global warming will not be characterized by more high temperature records. Instead it will be characterized by a loss of night time cooling.

Conclusion: The rate that record temperatures are being set, (as well as record rain or drought) is an indicator of environmental stability. And that rate currently implies some type of instability.

Part 5: Secondary Effects & Chaos

The predicted change in temperatures is small, in fact, its only about 2 degrees. A change that small is smaller than most people will really notice. The increase in atmospheric CO2, and an increase in temperatures will be barely noticeable to most people. Even though the changes seem small there may be large secondary effects.

Large scale changes in the water cycle may occur bringing floods to some areas and droughts to others. The climate, as evidence suggests, may become more chaotic oscillating between drought and deluge. Instead of a weekly cycle of rain and sunshine, we have long spells of extreme rain and long spells of drought. If these patterns become more severe many farms may become unproductive.

A major part of the human population has become dependent on industrialized farming and food distribution methods. Farming is critically dependent on stable environmental patterns. Long term changes in any of the following could catastrophically reduce food production:

  • the the weekly rate of rainfall
  • the time of year that rainfall occurs
  • the temperatures during the summer
  • the temperatures during the winter
  • the temperatures at night

Approximately 300 million people are dependent on the food produced in the American West. Many of the alternative locations for growing food have been buried under human developments. If a change in climate should undermine the ability of the American West to produce food (e.g.: a drought lasting more than one year) then 300 million people would be forced to seek other sources of food.

If the polar ice caps melt, and they are currently melting faster than predicted, coastal flooding and storms will ensue. People who live in coastal areas, or depend on trade that occurs in coastal areas will have to adjust.

There is evidence that tropical warming has historically resulted in epidemics. If this is accurate, then we will face an increased rate of epidemics.

Environmental change, heating, droughts, fog, rain, etc. may change faster than the species in those ecosystems can adjust. If any ecosystem that we depend on, directly or indirectly, then we will have to make the adjustments.


The secondary effects of atmospheric change will most likely have a far greater impact on human life than the change in CO2 itself. We do not yet know what all the secondary effects will be.

Part 6: Overall Conclusions

  1. The increasing human population makes us increasingly vulnerable to environmental change of any type.
  2. Even if humans are not causing the environmental change, we will still need to be able to respond to the changes.
  3. Unbalanced human activity will eventually have long term environmental consequences.
  4. We will probably not see the changes until after too much damage has already been done.

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