Name:___________________________________
Unit 2 Project: General Vehicles Company
Engine Emissions and Air to Fuel Ratio
Combustion Overview:
When combustion happens in an automobile engine, the chemical energy is released
and used to propel the vehicle. The combustion process seems simple; however, is
quite complicated. On the surface, gasoline mixes with air in the cylinder of the
engine that is then ignited with a spark. This results in heat and pressure that is
used to power the vehicle. Under the surface there is a lot of chemistry happening.
Gasoline is a hydrocarbon (HC) and air is a mix of oxygen (O2), nitrogen (N2), and a
small amount of other gases. When combustion happens, the ideal result is that the
hydrocarbons react with the oxygen to form harmless water (H2O) and carbon
dioxide (CO2). These elements would then leave through the exhaust along with the
nitrogen. All of these byproducts do little to no harm to the environment. The
problem is ideal is not real. Sometimes other elements are released through the
exhaust. These elements are harmful to the environment and discussed below:
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Hydrocarbons (HC) – Hydrocarbons are released from unburned or partially
burned gasoline. These elements are responsible for smog. They are also
toxic so they can cause liver damage and cancer.
Carbon Monoxide (CO) – Carbon Monoxide occurs when the carbon atoms
react with only one oxygen atom instead of two. This element can have
adverse effects on the body and could lead to death if overexposed.
Nitrogen Oxides (NOx) – Nitrogen Oxides occur when the nitrogen reacts
with the oxygen. These elements are pollutants.
Air to Fuel Ratio (AFR):
The amount of air and gasoline that are mixed in the cylinder play a major role in
limiting the harmful emissions during combustion. An engine has an ideal ratio of
air to gasoline that takes many aspects into consideration:
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The amount of harmful emissions
Fuel economy
Power
Driveability
An ideal AFR finds the best blend of limiting harmful emissions, fuel economy,
power, and improved driveability. Suppose an engine uses an AFR of 18. This
means that it uses 18 parts air to one part gasoline. If an engine uses a “richer” AFR
than ideal (i.e. increase the amount of gasoline), then fuel economy decreases and
some harmful emissions also increase. If and engine uses a “leaner” AFR than ideal
(i.e. increase the amount of air), then power and driveability decrease and some
harmful emissions increase.
Task 1: Research
Your first task is to come up with what you think is the ideal AFR based on the
engine specifications provided. You will then write a letter to GV (General Vehicles)
explaining your findings and your suggested AFR.
Data Analysis
Tests were done on a GV engine at different AFR’s and exhaust results were taken
for the three harmful elements.
1. Hydrocarbons - The data collected for hydrocarbons showed a minimum of
85 parts per million at an AFR of 16.
2. Carbon Monoxide – The data collected in the study found that carbon
60
monoxide emissions in terms of the AFR fit the curve 𝑐(𝑥) = (2.8)𝑥−10.2 + 0.4,
where x is the AFR and c(x) is the % of CO.
3. Nitrogen Oxides – The data collected in the study found that the NOx
emissions in terms of the AFR fit the curve 𝑛(𝑥) = −5𝑥 3 + 3857𝑥 − 38411,
where n(x) is the amount of NOx in parts per million and x is the AFR.
Work
a) Write an equation for the hydrocarbon emissions in parts per million in
terms of the AFR ratio if another data point was 145 parts per million at an
AFR of 11 and it fits a quadratic model.
b) Because of government efficiency policies, the amount of emissions has to be
below a certain level. The amount of HC has to be below 100 ppm, NOx has to
be below 2569 ppm, and CO has to be below 2%. Figure out the possible
domain of AFR for each element. Solve HC and NOx algebraically (by hand).
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HC:
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NOx:
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CO:
c) Accurately draw each of the element curves on the graph provided. Use the
table feature of your calculator to help find a number of points to plot.
d) After studies were done on AFR and its effect on power, fuel economy, and
driveability, it was found that when the AFR was between 13 and 16.5 there
were favorable results in all three categories. Show this information in the
graph above by lightly shading this favorable portion.
e) Write a letter to the GV motor company explaining what you feel the ideal
AFR is to best meet all requirements discussed (HC, CO, NOx, power, fuel
economy, and driveability). Be specific and reference your work. Remember,
this is a professional letter and must be written as such. It should be a
maximum of one page single-spaced.
Task 2: Company Profit
After some research of their own, the U.S. government decided that the best
automobile engine AFR is 14.7. They came up with a system for penalizing
companies that did not meet this AFR standard. This system has two multipliers.
One of the multipliers is called the AFR multiplier. This is found by taking the
difference of the company’s average AFR and 14.7. The other multiplier is the
penalty value multiplier. This is found by multiplying the AFR multiplier by 15
billion.
f) Fill in the table for the missing multiplier values:
Avg. AFR
AFR
Multiplier
Penalty
Value
Multiplier
(millions)
14.4
14.5
14.6
-0.1
14.7
0
14.8
14.9
15
0
g) The annual penalty given by the government is equivalent to the product of
the AFR multiplier and the penalty value multiplier. Write an equation for
the penalty (in millions) in terms of the AFR.
h) The yearly profit for GV without government penalties can be modeled by the
function 𝑃(𝑐) = −7500𝑐 2 + 30000𝑐 , where P(c) is the yearly profit in
millions and c is the number of cars sold in millions. GV is manufacturing
cars that have an average AFR of 14.9. Write a profit equation for GV keeping
in mind the penalty for having an AFR of 14.9.
i) Is it possible for GV to have a yearly profit of 30.2 billion dollars? Show all of
the algebra that led to your conclusion.
j) What is the maximum yearly profit and how many automobiles must be sold
in order to produce that profit? Please show all of the algebra that led to
your answer.