Team #16663
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Ride Like the Wind Without Getting Winded:
The Growth of E-bike Use
Executive Summary
The use of electric bicycles (e-bikes) have been on the rise. These electric vehicles are
especially popular in urban areas for commuting and popular in other areas as a means of
entertainment. E-bikes also provide many benefits over traditional means of transportation (cars,
public transportation): they are cheaper and more environmentally friendly among other things. This
report attempts to see the future of e-bikes as a viable means of transportation and if the amount of
e-bikes used will affect society.
To determine important variables, we ran a GLM regression analysis to compare bike sales
and our other variables. The GLM gave us variables that had a significant causation to E-bike sales.
Very significant variables were per-capita income (0.00739), bike cost (0.000936), great
environmental concern (0.0242), fair environmental concern (0.0272), and average cost of a car
(0.0182). Insignificant variables were little environmental concern, none environmental concern,
no/missing environmental concern, traffic congestion, and the cost of gas.
In the model it was determined that much of the rapid increase in annual bike sales from
2021-2022 was due to the tax credit of up to 1500$ passed by the federal government in March of
2021. This would increase the pool of potential buyers for e-bikes, but this increase would only be
temporary because the potential buyers would only increase in the time just after the tax credit was
passed. Therefore the slope of the e-bikes sold graph would decrease after passing the initial phase
of the tax credit. The number of bikes sold would, however, continue to increase because of several
other factors found to be significant by linear regression: Cost of e-bikes, GDP per capita, and Car
price. These factors most affect the sales of e-bikes in the US because the main barrier to American
Citizens buying e-bikes is the price point of the e-bike. Summarized, the number of bikes sold in the
US will continue to increase, but it will increase more slowly than the growth in 2021-2022. The
model shows that in 2025 1,219,801 e-bikes will be sold and in 2028 1,500,311 e-bikes will be sold.
The adoption of e-bikes in the US will lead to decreased carbon emissions and increased
health for citizens because of both increased air quality and physical activity. Decreased pollution is
due to the use of electricity as energy for e-bikes rather than fossil fuels for cars, motorcycles, and
other vehicles. This will in turn increase air quality which studies have shown has a greatly positive
impact on health. E-bikes also increase the amount of exercise performed which increases health
and life expectancy.
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Table of Contents
0 Introduction
3
0.1 Restatement of problem
3
0.2 Global Assumptions
3
1 Q1: The Road Ahead
4
1.1 Context
4
1.2 Assumptions
4
1.3 Variables
4
1.4 Model Development
5
1.4.1 Data Manipulation
5
1.4.2 Model creation
6
1.5 Model Evaluation
2 Q2: Shifting Gears
7
8
2.1 Context
8
2.2 Assumptions
8
2.3 Variables
8
2.4 Model Development
9
2.4.1
Regression
9
2.4.2 Percent change of Bike Cost
10
2.4.3 Percent change of car cost
11
2.4.4 Percent change of disposable income per capita
11
2.5 Model Evaluation
12
3 Q3: O the Chain
13
3.1 Context
13
3.2 Assumptions
13
3.3 Variables
14
3.4 Model Development
14
3.5 Model Evaluation
17
4 Discussion
18
5 References
19
6 Appendix
22
Team #16663
0
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Introduction
This section reiterates the different components of the problem along with their targets. This year’s
problems asked the following:
0.1
Restatement of problem
1. Create a model to predict growth in e-bike sales. Predict the number of e-bikes that will be
sold two and five years from now.
2. Consider one or more factors that may have contributed to e-bike growth and use
mathematical modeling to argue whether that factor (or factors) was a significant reason for
the growth of e-bike usage.
3. Quantify the resulting impacts on carbon emissions, traffic congestion, health and wellness,
and/or other factors you deem important.
0.2
Global Assumptions
These are assumptions that affect all of the models used.
1. US Market only — The data used and models relate to the US market only.
2. Market stability — We assume that the US Market does not crash or boom in the next 5 years.
3. Market consistency — The data used in our models has a market that is neither over-saturated
or under-saturated. We can assume that there is no over-demand for e-bikes that would
result in a skyrocketing of prices or a saturation of e-bikes in the market that would result in
a sharp decline of prices.
4. Primary consumers of e-bikes are in urban areas — The majority of e-bike users are in urban areas.
Although a small portion of e-bike users are not in urban areas, they are not using their bikes
for daily commuting.
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1
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Q1: The Road Ahead
We will be focusing on the number of sales in the US along with other factors to determine a model
that can determine the amount of bikes sold in the future.
1.1
Context
The large increase in the popularity of e-bikes as a mode of transportation has created an explosion
on the e-bike market, especially in urban centers where e-bikes can be used to avoid heavy city
traffic. The cheap price of e-bikes, relative to cars, with relation to both actual price of the vehicle
and fueling, makes e-bikes an attractive option for many people needing to make relatively short
commutes. In addition to the environmentally friendly nature of the bikes, the pandemic has also
boosted e-bike sales.
1.2
Assumptions
1. Constant population — The number of people living in the US, barring a sudden migration or
other such event that is not likely, will mostly remain constant over the next 5 years. The
fluctuation of population is negligible.
2. Population density — In conjunction with a constant population, the population density over
the next 5 years will remain constant as well and any small fluctuations are negligible.
3. Market stability — Currently, the e-bike market is fragmented with no major company owning
the majority share of the market. We assume a relatively stable market that will not result in
an abnormal boom for our model.
4. The statements made in section 2 are correct — Section 1 relies heavily on many of the statements
made in section 2. The statements will be explained in more detail in their respective
sections, along with the assumptions that were made for those statements.
5. The model is focused on data points that are solely monetarily based — It is incredibly difficult to
mathematically predict the behavior of humans. Therefore, only data points based in tangible
monetary values were used.
1.3
Variables
Symbol
𝑡
Definition
Years passed since 2012
𝐶𝑏𝑖𝑘𝑒(𝑡)
Function that relates time to the percent increase in cost of
e-bikes.
𝐶𝑐𝑎𝑟(𝑡)
Function that relates time to the percent increase in cost of cars.
Units
Value
Years
14, 17
%
change
-
%
-
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change
𝐶𝐺𝐷𝑃(𝑡) Function that relates time to the percent increase of GDP of the
US.
𝐵 (𝑡)
The final model that determines the amount of e-bikes sold in
relation to time.
1.4
Model Development
1.4.1
Data Manipulation
%
change
-
Bikes
-
We selected data and slightly modified the data sets doing the following:
1. Combining data provided for Q2 of problem: bike sales(Q1), per capita disposable income,
environmental perceptions, average price of gasoline, battery cost and energy density, and
gas prices.
2. Removing all data before 2012 due to the recent emergency of the e-bike industry and lack
of e-bike sales data prior to 2012.
3. Finding datasets for variables that would impact bike sales: average price of bikes, cost of
electricity, CPI of vehicles, cost of vehicles, and traffic congestion.
a. Average price of bikes was calculated through a model of changes in Lithium Ion
battery costs [2.4.1].
b. Electricity cost in urban areas was calculated through average consumer price index
of electricity (CPI).
c. Price of vehicles in urban areas was calculated through the average CPI of vehicles.
d. Traffic congestion was calculated through average congestion duration in urban
areas.
Table 1: Data table containing the first half of the data analyzed
Fair
amount
(%)
Only a
little
(%)
Not at all
(%)
No
opinion
(%)
Average
price of
regular
grade
gasoline
(USD per
gallon)
Environmental Concern
Year
Per-capita
Disposable
Personal
Bike Sales
Income
Great
(units in
(USD)
deal (%)
thousands)
2012
70
39732
37
36
19
7
1
3.62
2013
159
38947
36
33
23
8
0
3.51
2014
193
40118
31
35
24
10
0
3.36
2015
130
41383
34
34
22
10
0
2.43
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2016
152
41821
42
31
19
7
0
2.14
2017
-
42699
47
30
16
7
1
2.42
2018
369
43886
42
30
20
8
0
2.72
2019
423
44644
47
27
18
8
0
2.6
2020
416
47241
43
26
22
9
0
2.17
2021
750
48219
46
29
15
9
0
3.01
2022
928
-
44
27
18
10
0
3.95
Table 2: A continuation of the data sets in Table 1
Year
Cost
(US$/kW-hr)
Gravimetric
energy
densities
(W-hr/kg)
Average cost Traffic
of vehicles
congestion
(USD)
(hour: min)
Cost of
e-bikes
(USD)
Cost of
electricity
(US$/kW-hr)
2012
-
-
$30,500
3:58
2070
-
2013
-
240
$31,250
4:19
2062
0.132167
2014
-
-
$33,500
5:06
2055
0.137083
2015
350
-
$34,000
5:13
2049
0.138083
2016
-
-
$34,450
4:45
2044
0.135167
2017
-
-
$34,670
4:29
2038
0.13775
2018
-
-
$35,610
4:21
2032
0.13625
2019
-
-
$36,820
3:43
2026
0.136333
2020
-
-
$38,960
-
2020
0.135333
2021
-
-
$42,380
-
2013
0.14075
2022
-
-
$49,507
-
2007
0.1585
1.4.2
Model creation
One of the main factors in determining the model for Q1 was the US government tax credit which
was passed in March of 2021. The tax credit refunds $1,500 or up to 30% of the bike's cost if the
bike costs less than $4,000. This tax credit encouraged US citizens to buy e-bikes, and was
responsible for the massive initial spike in e-bike sales in 2021-2022, and is the reason why the
change between 2022-2023 was significantly less. This means that as time goes on the slope of the
graph will continue to decrease. Due to this the regression model was chosen to account for the
passing of the initial buying craze over e-bikes.
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Equations using the data were made relating the subject of the data to the percent change of the
subject over time. This process is detailed in Section 2. The “factor” functions are added to the
function in order to keep the units in bikes (just adding does not modify units). The constant
multiplied by 𝑡 is used to make the units of the functions (a percent) into the correct unit (bikes).
The exception to this is the function of 𝐶𝐺𝐷𝑃(𝑡), which is used as a multiplier as GDP affects all
aspects of monetary things, which is what all the data points we used are based on. Again, this is
explained in more detail in section 2.
(
𝐵 (𝑡) = 𝐶𝐺𝐷𝑃(𝑡) 488 + 189(𝑡 − 9. 97)
1/3
[
]
[
+ 2. 96𝑡 100 ∗ 𝐶𝑏𝑖𝑘𝑒(𝑡) + 0. 059𝑡 100 * 𝐶𝑐𝑎𝑟(𝑡)
The final model uses the equation of the initial equation combined with the other factors that affect
bike sales. A graphing tool was used to create a regression model, which now includes the factor that
were determined to affect the model the most: the predicted change of e-bike prices. The predicted
number of bikes in 2025 and 2028 are as follows:
1.5
Year
Value (in thousands
2025
1219.801 e-bikes sold
2028
1500.311 e-bikes sold
Model Evaluation
The model takes into account both the logical reasoning for why bike sales would partially plateau in
the near future as well as showing how the most important factors would continue to spur on some
growth. The tax credit spurred a great increase in e-bike sales from ‘21-’22. However after this new
market of citizens had been exhausted the growth in bike sales would stagnate significantly. Several
factors which include the cost of e-bikes; the cost of their direct competitors, cars; and GDP per
capita. What this model does not take into account though is the somewhat less significant factors.
For example, the attitude towards environmental concern and the amount of infrastructure
supporting e-bikes is not taken into account. Additionally, this model relies heavily on many
assumptions that are not able to be proved to be true.
])
Team #16663
2
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Q2: Shifting Gears
In this section, the various factors affecting the amount of bike sales are determined.
2.1
Context
Many factors affect the need and want for e-bikes in relation to commuting. The price of bikes,
electricity, and other such factors need to be accounted for when creating a model. Additionally,
factors such as bike lanes, easily accessible bike storage, and other such infrastructure needs to be
taken into account. People are also social creatures: the “coolness” of e-bikes as well as the effect
they have on society (environment, traffic, etc.) is an important factor.
2.2
Assumptions
1. The constants used are the right units to result in the monomial being in the unit “bikes” — Admittedly,
this is a large assumption, however it is necessary for the model to work.
2. E-bike prices are primarily affected by the cost of their batteries — Metallurgy (frame, wheels, etc.) and
motors are not the primary cost of e-bikes nor are they changing in cost all that much and
are therefore negligible. However, batteries are constantly improving, both increasing their
energy density and decreasing cost simultaneously.
3. Energy cost will remain relatively constant — In the past years, energy costs have fluctuated
slightly, but not drastically increased or decreased over the past year, making the energy cost
as a factor basically negligible.
4. Increase in the number of E-bikes sold represents the growth in E-bike popularity — Based on the
assumptions made in 3.2 and the provided data, an increase in bike sales represents more
people switching to E-bikes and an increase in popularity.
2.3
Variables
Symbol
𝑡
𝑐𝐿𝑖
𝑏𝐿𝑖%
C
Definition
Units
Value
Years
-
Dollars
-
Percent of bikes that has lithium ion batteries
%
-
% cost of a bike compared to price in 2012
%
-
Years passed since 2012
Change in cost of lithium-ion battery
Team #16663
2.4
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Model Development
We used a GLM to determine the important factors to add to the predictive model. The following
sections describe the process of determining the equations and factors deemed necessary.
2.4.1
Regression
The regression was done in Rstudio and used the data mentioned in Tables 1 and 2. Rstudio was
used because it offers a wide variety of statistics-related libraries and provides a favorable
environment for statistical computing and design. In addition, the R programming language is
trusted and used by many quantitative analysts as a programming tool since it's useful for data
importing and cleaning. A general linear model (GLM) was then used on the data to compare
another variable with the number of E-bikes sold since Q2 wanted to find the “factor(or factors)
[that] was a significant reason for the growth of e-bike usage.” Therefore a GLM was determined to
be the best way to find statistical significance between any independent variable and the number of
bikes sold, where bikes sold were equivalent to the growth of e-bike usage and popularity. GLM
models help build a linear relationship between the response and predictors, even though their
underlying relationship is not linear. This is made possible by using a link function, which links the
response variable to a linear mode such that bike sales are the dependent variable of other variables.
The advantages of using a GLM are 1) the response variable can have any form and does not require
a normal distribution, 2) it can deal with categorical predictors, 3) is relatively easy to interpret and
allows a clear understanding of how each of the predictors is influencing the outcome, and 4) it is
less susceptible to overfitting than for example Classification Tree Algorithms(CTA) or Multivariate
Adaptive Regression Splines( MARS algorithms). A Gaussian family was then run with the GLM. A
Gaussian family is how R refers to the normal distribution and is the default for a “glm()” whereas a
Poisson family is used for non-normal distribution. The data only had points from 2012 to 2022 and
both E-bike sales and the comparative variables were continuous. Our team determined that there
weren’t enough data points to have a significantly varied distribution, therefore no specialized
families, such as Binomial or Poisson, were considered. Applying a summary to the GLM function
gave us significant variables through P values ( “Pr(>|t|)”). The p-value serves as an alternative to
rejection points to provide the smallest level of significance at which the null hypothesis would be
rejected. Meaning a smaller p-value signifies that there is stronger evidence in favor of the alternative
hypothesis and vice versa. The null hypothesis assumes any experimentally observed difference is
due to chance alone, and an underlying causative relationship does not exist so a low p-value
signifies that a chance relationship between the two variables is low and more likely a
cause-and-effect relationship. Any variable with a P-value less than 0.05 would be significant. Our
regression analysis showed that per-capita disposable income and cost of E-bikes were very
significant; average cost of a car, great environmental concern and fair environmental concern were
significant; and none environmental concern, no/missing environmental concern, traffic congestion,
cost of electricity, and cost of gas were not significant to E-bike sales.
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Table 3: Variable name and P-value
2.4.2
Variable Name
P-Value
Per-capita Disposable Income
0.000739
Cost of E-Bikes
0.000936
Average Cost of a Car
0.0182
Great Environmental Concern
0.0242
Fair Environmental Concern
0.272
Little Environmental Concern
0.0677
None Environmental Concern
0.589
Traffic Congestion
0.339
Cost of Electricity
0.108
Cost of a Gas
0.603
Percent change of Bike Cost
Using linear regression it was determined that the most significant factor in determining bike sales
was the price of the bike.
This model predicts the cost of an e-bike.
𝑏
2
% of e-bikes that use LI batteries = 𝑏𝐿𝑖%(𝑡) = 𝑡 = 0. 11007 + 0. 00217391 𝑡
Cost of a Lithium-Ion battery = 𝑐𝐿𝑖(𝑡) =
4
− 107. 012 +
(
4
𝑐(𝑥)
(
5412.12
𝑡+10.5794
)
)( )
𝑐(𝑥)
Average cost of an e-bike = 𝐶(𝑡) = ⎡ 10 − 10 ∗ 𝑐(0) 𝑐(0) ⎤ ∗ 𝑏𝐿𝑖%(𝑡)
⎣
⎦
Percent change of cost of e-bike based on years since 2012:
𝐶𝑏𝑖𝑘𝑒 =
𝑐𝐿𝑖(𝑡)
𝑐𝐿𝑖(0)
·
(
4
10
−
4
10
( ))
𝑐𝐿𝑖(𝑡)
𝑐𝐿𝑖(0)
· 𝑏𝐿𝑖%(𝑡)
The foundation of this model relies on the assumption that the main price change in e-bikes will be
the battery. The first step was to find what type of batteries e-bikes use. The types of batteries used
by e-bikes are mainly Lithium-Ion and Lead-acid batteries, there are a few others but they are not
especially relevant to the calculations. The price of lead-acid batteries, as well as most of the other
types, remains constant, while the price of lithium-ion batteries is decreasing. The percentage of
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Page 11
e-bikes that use lithium-ion batteries was then found. The current percentage of LI batteries is 25%
and by 2028 it is projected to increase all the way up to 60% by 2028. Because companies would be
more and more likely to adopt lithium ion batteries as time went on a quadratic function was chosen
to represent the percentage of e-bikes utilizing lithium ion batteries - 𝑏𝐿𝑖%(𝑡). Next was to
determine how the cost of a lithium-ion battery changes over time. The model that was created is
based off of a rational regression model using data from the last 10 years of lithium-ion battery
prices. The next step was to determine what percentage of the cost of manufacturing an e-bike was
dependent on the battery, as it turns out that number is about 40%, or
4
10
. The final model
measures the percent change in cost of an e-bike based on years since 2012. The percent change in
lithium-ion battery cost since 2012 is represented as
𝑐𝐿𝑖(𝑡)
𝑐𝐿𝑖(0)
. Because it was determined that 40% of
the cost of an e-bike is in the battery initially it makes sense that the cost of the battery would be the
initial percentage minus the percentage decrease in battery cost. Then the percent of cost in the bike
would be multiplied by the percent of e-bikes that use lithium-ion batteries. So this expression
(
4
10
−
4
10
( ))
𝑐𝐿𝑖(𝑡)
𝑐𝐿𝑖(0)
· 𝑏𝐿𝑖%(𝑡) represents the percent of e-bike price which is dependent on
lithium-ion batteries. and then that would again be multiplied by the percent change of lithium-ion
battery cost to find the percent change in cost of the total box. In the overall equation it was
determined that for every 1% decrease to the average price of e-bikes 6 thousand more e-bikes are
sold.
2.4.3
Percent change of car cost
𝐶𝑐𝑎𝑟(𝑡) =
− 45. 4 + 0. 031(𝑡 + 1500)
As car costs increase, less people would buy cars and search for alternative methods of
transportation. The inverse is also true, as car prices decrease the amount of people buying cars
would increase. This means that the potential customers for e-bikes, and therefore e-bike sales, are
inversely proportional to the price of cars. This model was calculated using linear regression on car
price data. Linear regression was used because car price increase has been generally linear in the
recent past.
2.4.4
Percent change of disposable income per capita
𝐶𝐺𝐷𝑃(𝑡) = 0. 948 + 0. 022(𝑡)
As US GDP per capita increases US citizens would have more disposable income, which means that
the chance each citizen could afford an e-bike would increase. This increases the potential sales for
e-bikes in the US. This model was again calculated using linear regression because GDP per capita
has been increasing steadily in the US.
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2.5
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Model Evaluation
After considering the factors which we thought could affect the number of e-bikes sold in the U.S.,
we ran general linear models of each of these factors using provided data sets along with data we
gathered. These models outputted a statistical 𝑝 value which allowed us to isolate the statistically
significant factors (those with values ≤ 0. 05). We were then able to run regression models for each
of these factors, finding equations for each one to then create a general equation 𝐵 (𝑡).
Despite being able to account for the significantly significant factors, we were unable to incorporate
all possible factors into our model. This resulted in a model that was not as accurate as it could have
been. Also, by choosing to run lots of regression models, our final function and predictions may not
have been completely representative of all the data points.
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3
Page 13
Q3: O the Chain
The increase of e-bikes being used will have large effects on society. This section attempts to model
and quantify these effects.
3.1
Context
With every change, there is something that the change will affect. This cause and effect chain also
applies to the increase of the use of e-bikes for commuting. These effects include a reduction in
carbon emissions, decreased traffic congestion, and health benefits of using bikes. The increase of
e-bikes will also change the infrastructure of the US, with e-bikes beginning to replace traditional
modes of transportation like buses and cars.
3.2
Assumptions
1.
2.
3.
4.
5.
6.
7.
8.
The model created in section 1 is correct — all of the equations based are based off of the model
determined in section 1.
Carbon emissions from production of everything except frame, tires, and batteries for a bike are negligible —
The frame, tires, and batteries for a bike are the primary contributors to carbon emissions.
The rest of the materials/parts do not produce a lot of carbon.
Every e-bike frame is made entirely of aluminum – The vast majority of e-bikes have aluminum
frames. Thus, it is more appropriate to simply assume that all frames are completely
aluminum, rather than accounting for every single trace metal and alloy in a select few
e-bikes.
The ratio of frame size, frame mass, and tire size between standard bikes and e-bikes will be equal –
Given that both types of bike have extremely similar proportions, one can safely assume that
the ratio of dimensions such as frame size, frame mass, and tire size are all equal
Each e-bike purchased will replace an automobile on the road — Only consumers with a commute
less than 10 miles one way will replace their vehicle with an e-bike.
The vast majority of the average American’s driving is their commute – The average American spends
most of their time either at work or at home, and thus the majority of their driving will be
between those two locations, i.e. commuting.
Weather will not have an impact on consumer choice — Weather is varied and inconsistent and
depending on the season will affect consumer choice. Since the scope of the model is over
years and not months, the weather will not affect the results. Additionally, it is assumed that
there will be no major changes in weather patterns nor a large-scale natural disaster.
The health benefits of switching to e-bikes will be evenly distributed over the e-cycling population – Given
that these calculations will be based on averages, we assume that these benefits, both in
terms of exercise and less air pollution, will be evenly distributed to all.
Team #16663
9.
3.3
Page 14
The vast majority of air quality issues in London and Mexico City are caused by car use – Both of these
cities have relatively small manufacturing sectors, and relatively few causes for air pollution
aside from the use of cars.
Variables
Symbol
Units
Value
Years passed since 2012
Years
—
𝑃𝑃(𝑡)
Pollution caused by the production of new e-bikes
Kg of
CO2
—
𝑃𝐸(𝑡)
Pollution caused by the electricity use of e-bikes
Kg of
CO2
—
𝑃𝐶(𝑡)
Pollution caused by the use of gasoline by cars
Kg of
CO2
—
𝑃𝑡𝑜𝑡(𝑡)
Total pollution
Kg of
CO2
—
𝑡
Definition
𝑤(𝑡)
Health benefits of exercise due to e-bikes
Microlives
—
𝑎(𝑡)
Health benefits of lessened air pollution due to e-bikes
Microlives
—
ℎ(𝑡)
Total health benefits to a single e-cyclist due to e-bikes
Microlives
—
3.4
Model Development
Whenever an e-bike is purchased, it must have been produced at some point earlier. The extraction
and refinement of the resources required to produce a single e-bike releases a certain number of kg
of carbon dioxide (kg CO2) into the atmosphere, causing damage to Earth’s environment, per single
e-bike produced. There are three main components of the e-bike that will produce a non-negligible
amount of CO2 in its production: the aluminum frame, the tires, and the battery.
The ratio of the size of a standard bike to that of an e-bike for someone that is 5’1” tall is 5:6, or
0.833. The average aluminum bike frame has a mass of 1.36 kg. Thus, by assuming that the ratio of
size and mass are similar given the constant density of aluminum, the mass of aluminum in the
average e-bike frame can be determined. By then multiplying this by the average kg CO2 released per
kg Aluminum produced, the amount of pollution in constructing the frame can be determined to be:
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15
𝑃𝑓 = ( 18 )(1. 36)(2) = 2. 67 kgCO2 per e-bike
The mass of the average road bike tire is about 1 kg. The number of kg CO2 produced per kg of
rubber harvest from cultivated land is 0.975 kg CO2. Thus, the pollution created by producing a
single e-bike with two tires comes to:
𝑃𝑡 = (0. 975)(1)(2) = 1. 95 kgCO2 per e-bike
The vast majority of the pollution released by the production of an e-bike comes from the
production of its battery. This figure depends on the type of battery used. As mentioned before, the
two primary battery types for e-bikes are lithium-ion and lead-acid batteries. For every metric ton of
lithium mined, on average, 15 metric tons of CO2 are produced. The ration holds true at the
kilogram level. Due to both carbon released through mining and through forging, the production of
the aluminum required for an 80 kilowatt-hour battery will result in, on average, 9,200 kg CO2.
Given that the amount of lithium for a lithium-ion battery required per kWh is relatively constant,
the production of pollution per 0.65 kWh lithium-ion battery, an average for e-bikes, is:
𝑃𝐿𝑖 = ((9200)/80) * 0. 65 = 74. 75 kgCO2 per e-bike
As for the production of lead-acid batteries, it has been found that the production of a single
lead-acid battery of a certain power, on average, causes the release of twice the amount of CO2 as
the lithium-ion battery of that same power. Thus, the pollution per 0.65 kWh lead-acid battery is:
𝑃𝐿𝐴 = 74. 75 * 2 = 149. 5 kgCO2 per e-bike
In order to find the total pollution due to the battery, both figures are multiplied by their respective
percentage of total e-bikes. The percentage of lithium-ion batteries was determined in Q1, and the
percentage of lead-acid can be determined simply by subtracting the percentage of lithium-ion from
one:
𝑏𝐿𝐴%(𝑡) = 1 − 𝑏𝐿𝑖%(𝑡)
𝑃𝐵 = (𝑏𝐿𝑖%(𝑡))(74. 75) + (𝑏𝐿𝐴%(𝑡))(149. 5)
Finally, the total pollution released by producing e-bikes, per bike, can be found by adding the
pollution due to each individual part and then multiplying that sum by the function of bikes
produced, yielding the total pollution due to production of all new bikes:
𝑃𝑃 = (𝐵 (𝑡))(2. 67 + 1. 95 + (𝑏𝐿𝑖%(𝑡))(74. 75) + (𝑏𝐿𝐴%(𝑡))(149. 5)) kg CO2
Another source of pollution from these bikes is their electricity consumption. While they do not
pollute in their operation, they require electricity that could come from a polluting source. It cannot
be determined which source every single charge comes from, however it is reasonable to break it
down along the lines of the US’s total power production. 31.8% of its electricity is produced by
burning natural gas, 28% from petroleum, 17.8% from coal, and 22.3% from nuclear and renewable
sources. The kg CO2 released by burning 1 kWh’s worth of natural gas is 0.44 kg, for petroleum it is
1.11 kg, and for coal it is 1.03 kg. Nuclear and renewables produced a negligible amount of CO2.
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The average range for a 1 kWh battery is 65.98 km. Thus, the pollution produced per kWh for an
electric bike is:
𝑃𝐸 = ((0. 44 * 0. 318) + (1. 11 * 0. 28) + (1. 03 * 0. 178))/(65. 94) = 0. 015 kg
CO2 per kilometer
However, in order to properly apply this, it must be put in terms of time. This can be achieved by
putting it in terms of the distance traveled (i.e. power used) per year. Given that the optimal
commuting range for an e-bike is 10 miles or less, it was determined that Americans with commutes
that distance would be the primary purchasers and users of e-bikes. The average commute length for
an American is 20.5 miles one way, 27.8 minutes one way, and thus have an average commuting
speed of 44.244 miles per hour. Thus, a commute of 14 minutes or less is the threshold for the
optimal commute for an e-bike. Out of this group of commuters, 52% have a commute from 10 to
14 minutes, and 48% have a commute less than 10 minutes. Assuming that the average commute in
each group is the average of every whole number in the data set, then 52% will have commutes of 12
minutes, and thus 8.85 miles (14.23 km), and 48% will have commutes of 5 minutes, and thus 3.69
miles (5.94 km). This data can then be multiplied by the kg CO2 per kilometer, multiplied by 365 to
apply for an entire year, and then multiplied by B(t) to cover the entire pollution generated by the
use of e-bikes:
𝑃𝐸(𝑡) = (𝐵 (𝑡))(0. 015)(365)((14. 23 * 0. 52) + (5. 94 * 0. 48)) = 56. 72𝐵 (𝑡) kg
CO2
Additionally, some CO2 emissions are actually prevented by the use of e-bikes, in terms of them
replacing cars. The average American car produces 4600 kg CO2 per year of standard driving. This
can be multiplied by B(t) to find:
𝑃𝐶(𝑡) = 4600𝐵 (𝑡) kg CO2
The total pollution change over time, as related to e-bike use, is:
𝑃𝑡𝑜𝑡(𝑡) = 𝑃𝐵(𝑡) + 𝑃𝐸(𝑡) + 𝑃𝐶(𝑡)
A second primary effect of the increased sales of e-bikes will be an increase in average health and
wellness of users. This was measured in microlives, a unit of risk for specific activities that results in
an average increase of 30 minutes for one’s lifespan.
The first source of health is increased exercise and decreased sedentary activity. Given that, using the
commuting data from earlier in this section, the average e-bike commute one way is 18 minutes, and
that 20 minutes of physical activity results in the gain of 2 microlives, one gains 4 microlives per day
from the additional activity. Additionally, the sedentary activity of sitting in a car is lost. Given that
the same commute by car is, on average, 10 minutes, and that 2 hours of sedentary activity results in
the loss of 1 microlife, one loses
2
12
microlives per day from driving. The individual gains this
benefit per every year they spend having purchased the e-bike.
2
𝑤(𝑡) = (4 * 365)𝑡 − (( 12 ) * 365)𝑡 = 1399. 17𝑡 microlives
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Additionally, one benefits from the lack of air pollution due to cars. Living in the air of Mexico City
1
as opposed to the air of London results in the loss of ( 2 ) microlives. Mexico City has roughly
3,000,000 cars, while London has 2,648,000 cars. The difference is 352,000 cars. Assuming that this
air quality difference is mostly due to cars, an increase in 352,000 e-bikes results in the decrease of
1
the same number of cars and the gain of ( 2 ) microlives, then the health benefit from increasing air
quality is thus:
𝑎(𝑡) =
𝐵(𝑡)
2(352000)
microlives
Thus, the total health benefit due to the sale of e-bikes is thus:
ℎ(𝑡) = 1399. 17𝑡 +
3.5
𝐵(𝑡)
704000
microlives
Model Evaluation
This model contains both its strengths and its weaknesses. In terms of strengths, it is able to take in
numerous di erent factors and subtleties in terms of the impact of the sale of e-bikes. It is able to
account for the entirety of the carbon-based pollution caused by the sale of e-bikes and the replacement
of cars on the streets. Additionally, it is able to demonstrate the copious health bene ts, both due to
physical activity and improved air quality.
However, it does have numerous drawbacks. Firstly, it makes many assumptions. Some, such as the
majority of carbon emissions from the production of e-bikes being derived from the production of the
frame, tires, and batteries, are quite realistic. However, some are less so. Particularly problematic is the
assumption that all e-bike purchases will result in the replacement of a car on the road. This
assumption was made partially due to the rationale that consumers will only purchase e-bikes if they
don’t already have bikes and wish to travel without the pollution of a car, and also on the convenience
of that assumption and the extreme di culty in otherwise assessing the impact of e-bike sales on
carbon emissions. Another problematic assumption lay in only using the commute as a standard for
how much CO2 emissions will be saved, given that cars are used for many other purposes. However, the
daily commute was the only activity with nearly as much information on it as did.
Finally, the scope of this section was somewhat limited; only carbon emissions and health risks were
covered. It likely would have been much better to cover additional topics such as the impact e-bike sales
would have had on tra c patterns.
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Discussion
It has been found that the sale of e-bikes will slowly but surely increase as e-bikes become more
financially available to many Americans. The price of Lithium Ion batteries will decrease and market
share of Lithium Ion batteries will increase, the price of cars will continue to increase, and US GDP
per capita will continue to grow. All leading to an increase in the amount of Americans that can
purchase e-bikes. The adoption of e-bikes in the US will lead to decreased carbon emissions and
increased health for citizens because of both increased air quality and physical activity.
Possible future areas of study are how the human nature of a consumer will affect the model or how
the many assumptions made can be proven. Additionally, we can expand this model into more
effects caused by the rise of e-bikes.
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Appendix
(1) R Code of General Linear Model
Significant GLM Results
(2) GLM result for Per-capita Disposable Income
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(3) GLM result for the Cost of Bikes
Slightly Significant GLM Results
(4) GLM result for Great Environmental Concern
(5) GLM result for Fair Environmental Concern
(6) GLM result for Average Cost of a Car
Insignificant GLM Results
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(7) GLM result for Little Environmental Concern
(8) GLM result for None Environmental Concern
(9) GLM result for No/Missing Environmental Concern
(10) GLM result for Traffic Congestion
(11) GLM result for Cost of Electricity
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(10)
GLM result for Cost of Gas