Modeling Future Telephone Power Usage

This paper was co-authored with Eric DuBois of Rensselaer Polytechnic Institute.

Table of Contents

Summary

In this paper, we consider the energy efficiency of a cell phone system, as compared to that of a landline system, for a national telecommunications network. Over the past ten years, large numbers of landlines in the US have been replaced with cell phones, and this trend will probably continue for several decades into the future. We model the effects of this transition in terms of the energy consumed during phone use, during manufacturing, and for maintaining the infrastructure necessary to support communications. We also model how a landline or cell phone network would develop in an emerging country, the Pseudo-US, which does not yet have a significant telecommunications infrastructure.
We have found that the most important variable in terms of determining total energy usage is the number of cell phones or landlines per capita, and that this variable can be modeled with a logistical curve. Our data shows that logistical curves match current US numbers for both cell phones and landlines extremely well, with an R^2 value of over 0.99, and provide a plausible model for the development of a new network in the Pseudo-US. Our model for the present US shows that, although the transition from cell phones to landlines caused a temporary blip in energy usage, peaking in 2006 at 40.8 PJ/year, this will probably decline in the near future as more people discard their landlines. In addition, although we show that cell phones do use more power than landlines, in large part because the larger number of cell phones required for a given population, this effect is not very large; the power consumption of our US network model in 2020 is only 40.5 PJ/year, or 65% greater than total energy use in 1985, even though we predict that the US population will grow 44% during the same time period.
For an emerging country with no telephone infrastructure, the Pseudo-US, we predict that cell phones will also use a greater amount of energy over the period from now until 2060, with a total consumption of 1007 MBOE (million barrels of oil equivalent), as compared to 784 MBOE for landlines. However, we also predict that a network based off of cell phones can be implemented 79% faster than a landline-based network, primarily because of the enormous amount of static infrastructure which needs to be installed before landlines can function. We show that the power wasted by cell phone chargers, although nontrivial at 3.81 MBOE annually in the US in 2008, is comparable to the amount wasted by other consumer electronic devices, such as home theater systems and VCRs.

Introduction

The world is growing increasingly interconnected by wireless technologies. At the forefront of this revolution is the rapid development and adoption of cellular telephones. However, unlike traditional landline phones, cell phones require a constant supply of electricity, and may therefore increase our annual energy demands. Yet at the same time, cordless telephones, which require even more energy per day to function than cell phones do, have already replaced most traditional, corded landline phones, with a household penetration rate of 83% (Roth & McKenney, 2007).

So, which of the alternatives- landlines, cell phones or some combination thereof- is the most socially, monetarily, and, especially given the looming specter of peak oil and climate change, the most energy effficient model for communication?

Assumptions

  • While cell phones can continue to work effectively for around ten years (ignoring battery life), the turnover rate due to fashion and technological obsolescence tends to be closer to between two and two and a half years (Nokia, 2005).
  • The energy required parameter in each model should include all phases of phone use, from production to recycling, in addition to the creation and maintenance of the requisite infrastructure.
  • The cordless phone market is saturated and the number of cordless phones to landlines is constant.
  • We assume that, in addition to newly manufactured phones, consumers will use an equally large number of recycled phones, whether through resale, charity, ‘hand-me-downs,’ or other means.
  • The power drawn by each cell tower will be treated as constant, as changes in tower energy use and efficiency are effectively impossible to predict.

Cell Phone Adoption and Use in the Real United States

Cell Phone Power Consumption Model

The total energy consumed by the production and use of cell phone, Ic is modeled by:

Ic=(cp∙p)[Ic+Rc]2∙cT+E(ci)

We average the data for heavy and light users, found in the 2005 Nokia report (Nokia 2005), to find the inclusive power consumption of an individual cell phone, Ic=264 MJ. We find also from this report that the cell phone turnover rate, CT≈2 years. We model the total population using data and projections from the US Census Bureau.

Graph 1

Based on the number of cell phones in the US (US Census Bureau, 2008) and accounting for population the number of cell phones per capita, cp, can be modeled by the following graph:

Graph 2

The total energy used for a recycled cell phone, as opposed to a newly manufactured cell phone, is modeled by:

Rc=r+Ec

From the 2003 Skerlos report we have that the energy required to refurbish the phone, r≈1.2MJ and from the Nokia report we have that the energy consumed during actual use, Ec=89MJ. While we could take transportation into consideration, this would be hard to model within the US market where many phones passed on through charity or through family members. Finally, taking all these constants into account, we find Rc=90.2MJ.

To model Eci, the energy consumed by the cell phone infrastructure, we use:

Eci=t∙(p1000)∙E(t)

While Et, the power consumption of each tower, varies in practice, to simplify the model we will assume that for all towers, they draw 500W (UCSD, 2008). Given this, we find that Et=15,778MJ/year. Fitting an S-curve to the number of cell towers (CTIA, 2008) and dividing by the appropriate figures from the US population (US Census Bureau, 2008) we arrive at the following graph for t:

Graph 3

Taking all of this data into consideration for fixed constants, our model for the real United States simplifies to:

Ic=cp∙p∙(264MJ +90.2MJ)2∙2 years+[t∙p1000∙15778MJ/year]

=p[(cp∙88.55 MJ/year)+(t∙15.778 MJ/year)]

As p, cp, and t are all functions with time as their only parameter, it becomes relatively easy to model the power consumption of all cell phones inclusive of their infrastructure and manufacture.

Graph 4

Landline Power Consumption Model

The majority of the energy consumed by the landline infrastructure is used to produce and charge cordless phones. Hence, our model for landline power consumption is of the form:

Il=p∙lp∙wlM(w)wt+Ew

The term ‘p∙lp‘ should be familiar from the cell phone model- in this case representing the population function (graph 1) and the number of landlines per capita, respectively. The latter is modeled by the following graph (FCC, 2008):

Graph 5

As stated in the assumptions, we consider the cordless phone market to be saturated and thus, the number of cordless phones, w , to landline connections, l (FCC, 2008), to be constant at 1.219. Moreover, we know the yearly power consumption of a cordless phone, E(w), is, on average, 28KWh/year or 100.8MJ/year (Roth & McKenney, 2007).

To model the turnover rate of cordless phones, we divide the number of installed cordless phone bases, w, by the number of replacement phones sold annually in the United States.

wt=wwr

Where the number of replacement phones, wr=ws-(p2005-p2004[wp2005]). In other words, the number of replacement phones is the number of phones sold, ws (Sanchez, Webber, Brown, & Homan, 2007), minus the number of new cordless phone users from 2004 to 2005. We find that wr=53,298,000 given that ws=55,966,000 and ws=179,000,000. Consequently, we arrive at the figure for wt to be 3.36 years.

To determine the inclusive power consumption used in the manufacture of cordless phones, Mw, we compare the electricity used in the final production phase of the cordless phone, P(w), to that of the cell phone, P(c). We assume that the ratio between total power consumption, and the electricity used during the manufacturing process, is the same for both devices. Thus we have the formula:

Mw=M(c)P(c)∙P(w)

Deriving values from previous data (Andræ, Mölle, Anderson, & Liu, 2004) we find that Pc=16.7MJ and Pw=5.98MJ, and from the 2005 Nokia report we have that the inclusive manufacturing power consumption, including transportation, Mc=175MJ. Thus, we have that Ml=62.7 MJ.

Deriving a simplified equation from this data we arrive at:

Il=p∙lp∙1.21962.7MJ3.36years+100.8MJ/year

=p∙lp145.6MJ/year

This graphs out to:

Graph 6

Combined Power Model and Discussion

cFinally, we consider the total power consumption of both models cell phones and landlines combined or in other words, how much energy is being used to maintain our telephone communications system as a whole.

Graph 7

Based on the above graph, we conclude that although the actual transition from landline phones to cell phones creates a sizable energy demand, the cell phone system itself is not vastly more energy-intensive that the landline system. This is caused in large part by the advent of cordless phones which have made the landline system a far less energy efficient system than it had been previously.

In a one-on-one comparison, cordless phones are far surpassed in terms of energy efficiency by their more compact and energy-efficient cell phone brethren. In deriving our models, we found that a cordless phone requires 145.6MJ/year whereas a cell phone requires only a modest 88.55 MJ/year. Above all else, two factors burden the cordless phone with this notable inefficiency in comparison to the cell phone. The first is that while a cell phone has a quicker turnover rate than a cordless phone (2 years as opposed to 3.36 years for cordless phones), people see cell phones as especially valuable (Nokia, 2005) and are much more likely to recycle or reuse them. The second major contributor is that cordless phones draw about three times more power from the wall than mobile phones.

Why, then, does the cell phone system require more energy than the landline system? Simply put, there are far more cell phones than cordless phones. In fact in 2007, there were almost twice as many cell phones (255 million) (US Census Bureau, 2008) as there were cordless phones (179 million) (Roth & McKenney, 2007). In addition, cordless phones are generally cheaper and less-energy intensive to produce than cell phones. Finally, cell phones require a vast infrastructure of energy-consuming cell towers, which utilize a considerable sum of electricity.

Thus, from an energy perspective, landlines are the preferred phone system. Yet, mobile phones provide many social and economic benefits that are not present in a landline system. This will be covered later, when we consider the pseudo-United States.

Cell Phones vs. Landlines in the Pseudo-United States

We now consider the models for power consumption in terms of the pseudo-United States. As the pseudo-United States is assumed to have the same demographics and economic conditions as the real United States, the majority of the models will remain the same- population growth, power consumption per phone and turnover rates. The major difference comes from the adoption rates of landline and cell phone systems.

The only remaining variable, then, is the number of cell phones and landlines per capita. We assume that this variable can be modeled as a logistic growth function, with time as the dependent variable:

cp=A2+A1-A21+ex-x0dx

Where x is the year, and A1, A2, x0, and dx are the four model parameters. The number of landlines per capita can also be modeled in this fashion, with different values for A1, A2, x0 and dx. In order to fit values to these parameters, we make the following assumptions based on the data that we have obtained:

  • In 2008, the pseudo-US starts out with a penetration rate of .001 cell phones, or landlines, per person. This is the lowest level of phone penetration in any real, physical country as of 2001 (source), and so we assume this as a conservative lower bound.
  • The fastest possible growth rate for cell phones per capita is 225% annually, and the fastest possible growth rate for landlines per capita is 35% annually. Since we assume that the pseudo-US is as wealthy as the real US, there should be very few or no economic limitations on how fast the telephone network is installed. However, there are obvious physical limits on how fast a country can lay wires, build telephones, manufacture or import electronics, etc. We assume that this limit is 35% and 225% for landlines and cell phones respectively, as no large country has been able to achieve a faster growth rate than this, even during the height of the tech bubble from 1996 to 2001 (source).
  • At time minus infinity, the number of cell phones and landlines per capita can safely be assumed to be zero.
  • Eventually, the pseudo-US will reach a saturation point, where it is no longer economically worthwhile to install new phone lines, as access is already available essentially everywhere. The economy and demographics of the pseudo-US are assumed to be similar to those of the real US, so we can assume that the saturation points are also similar.

We fit the model parameters to this data using the following equations:

  • For the assumption that there are no cell phones or landlines at time minus infinity, we simply set A1 equal to zero:

A1=0

  • The saturation points for the pseudo-US can simply be copied from the saturation points in our model of the real US:

A2 landline= 0.796

A2 cell phone=1.1986

  • The limitation on the physical growth of infrastructure is somewhat trickier to model. The key here is that the logistic function we are using to model the growth in the telephone network approaches an exponential function as x approaches minus infinity. Hence, if we choose a function that approaches the function (1+gr)^x, where gr is the maximum growth rate, as x goes to infinity, the maximum percentage growth rate of our logistic curve will be equal to the maximum percentage growth rate that is physically possible to achieve. We do this by taking the derivative of the function and then dividing it by the original function, for both the logistic growth curve and the exponential function, (1+gr)^x, and then setting the resulting values equal to each other:

1y1dy1dx=1y2(dy2dx)

A2dx= ln(1+gr)

dx landline= 2.5497

dx cell phone=1.009

  • The final parameter is set by setting the logistic function equal to .001 at 2008, and then solving:

x0=2008-lnA1-A20.001-A2-1*dx

x0 landline=2024.94

x0 cell phone=2017.476

From this we arrive at the following graphs for cp and lp:

Graph 8

Graph 9

Based on our formulas, we predict that it would require roughly eight to ten years for the pseudo-US to create a fully developed cell phone network, as opposed to the 20 or 25 years required to create a landline network. The obvious problem with building a landline network is the enormous infrastructure required, which would need miles upon miles of wire, and an extensive base of skilled workers to create and maintain. Cell phones, on the other hand, require a substantial, but not nearly as large, network of cell towers to cover this same area.

The Energy Needs for Pseudo-United States (2009-2060)

Now that we have models for the adoption of cell phones and landlines in the pseudo-United States, we are able to use the original power consumption models to produce the following predictions for total annual power consumption1:

Graph 10

Graph 11

Whether the pseudo-Americans decides to adopt cell phones or landlines, or even some combination of the two, it is clear that they will have to quickly increase their annual imports and production of oil. To get a better understanding of how a combination of these two systems fares for power consumption we created a graph based on a combination of cell phones and landline phones with the left side dominated by cell phones and the right by landlines.

Power Consumption in MBOE for Combination of Systems

Graph 12

This only further proves our belief in the perspective that with cordless phones in existence, the cell phone network is not much more energy intensive than the landline network.

However, landlines do have certain advantages besides lower power consumption in their favor (Coombes, 2004).

  • Many outside services, such as DSL, require a landline connection.
  • Landline connections allow emergency officials to know exactly where the caller is located and respond appropriately.
  • For some businesses, it may be beneficial for customers to be able call a landline at the location.
  • For important conversations, landlines guarantee voice quality and no dropped calls.

On the other hand cell phones, too, have many benefits:

  • The most obvious benefit- Cell phones are mobile allowing individuals to bring their phone with them and stay in touch. This can be especially important if the individual has to be reached in an emergency but is not staying in just one place. Similarly, cell phones allow for individuals, such as hikers, to stay in contact in less developed areas.
  • They allow for picture messaging, texting, and other forms of data transfer.
  • Cell phones require a smaller more modular infrastructure.

Power Consumption of Cell Phones Based on Charging Technique

We have already seen how much electricity is required to maintain a cell phone system, but just how much of this is wasted? In considering this question, we will focus on two major causes of wasted electricity- overcharging of cell phones, and leaving the charger plugged in. In both cases, although the cell phone does not need energy, the charger still draws power. Thus, we use the following formula to model all the power wasted by cell phone chargers nationwide:

Annual Energy Waste=α∙pα+β∙pβ365.25(p∙cp)

Where α is the number of hours that the phone is in the charger but already charged, pais the energy used per hour when the phone is in the charger but already charges, β is the number of hours the charger is left without a phone, and pb is the power consumed by the charger when there is no load. Since most people never unplug their cell phone charger, we may safely assume that α+β+γ=24, where γ is the number of hours the phone spends actually charging.
From (Nicolaescu & Hoffman, 2001), we know that, for a third-generation cell phone, a reasonable, average value for is 1.77 W or 6.372 KJ/hr., and an average value for is 0.72 W, or 2.592 KJ/hr. We also know that the average cell phone spends two hours charging before the battery reaches its full capacity. Since Americans get roughly 7 hours of sleep every night (Moore, 2004), we may assume values of 6 and 16 for α and β, respectively. Hence, the annual wasted power works out to be 4.9186×1012 KJ/year, or 4.9186 PJ/year. Based on our model we can see how many barrels of oil are wasted every year by these practices:

Graph 13

Power Wasted by Standby Mode in the Real United States

Many consumer electronic devices, such as VCRs, home theater systems, and video game consoles, use energy even when they are performing no useful function. We break down this wasted energy into two parts: energy used by the device while in standby, sleep, or idle mode (but performing no function), and energy used by the device while it is turned off, but still plugged into the wall. We use the following equation to model the total amount of energy wasted per type of device:

Annual Energy Waste=d∙3.6∙Ewid∙Tid+Ewod∙Tod∙(4.83792×10-7)

where d is the number of devices that are currently in use in the US in millions, Ewid is the amount of energy in watts that the device uses while idle, Tid is the time in hours per year that the average device spends idle, Ewod and Tod are the energy used while and amount of time that the device spends off, respectively. 3.6 and 4.83792 ×10-7 are conversion factors( 3.6 is used to convert watts to kilojoules per hour, and 4.83792 ×10-7is used to convert gigajoules to million barrels of oil equivalent [MBOE]).

Name of device Number of installed units (millions) Hours in standby mode Power used during standby mode (W) Hours off Power used while off (W) Power wasted annually (PJ) Power wasted annually (MBOE)
Compact Audio Systems

76

730

16

7190

7

16.966

8.208

Cordless telephones (standalone)

123

2015

2.3

5695

3.1

9.870

4.775

Cordless telephones + answering machine

57

2015

2.8

5695

3.8

5.598

2.708

DVD players (standalone)

75

900

10

7590

2.3

7.143

3.456

DVD players (standalone + record)

10

900

15

7590

2

1.032

0.500

DVD players (+ VCR)

35

900

11

7590

4.5

5.551

2.685

Home theater in a box systems

25

730

34

6450

0.6

2.582

1.249

Computer monitors

90

875

1

6020

1

2.234

1.081

Desktop PCs

90

350

4

5456

2

3.989

1.930

Laptop PCs

39

935

2

5457

2

1.795

0.868

Cable boxes

77

0

0

6031

15

25.077

12.132

Satellite boxes

70

0

0

5521

14

19.478

9.423

Standalone DVR

2

0

0

6678

27

1.298

0.628

Answering machines (standalone)

25

4

8760

0

0

3.154

1.526

TVs (analog)

237

0

0

6900

4

23.548

11.392

VCRs

105

793

12

7811

4.5

16.884

8.168

Video game consoles

64

560

36

7795

0.8

6.082

2.942

Total

152.281

73.672

Table 12

From our data, we find that televisions, VCRs, cable boxes, satellite boxes, and stereo systems are, by far, the largest wasters of energy, with these five appliances accounting for 66.9% of the energy loss among all appliances studied. Cell phone chargers, although they use far less power while in use than most of these appliances, waste a comparable amount of energy to many of the more energy-intensive appliances, at 3.81 MBOE per year. This is primarily because, although cell phone chargers use less energy while in use than most other appliances, their energy use does not drop off very much when the phone stops charging; the amount of power consumed while idle is more than half of the amount of power used while the phone is charging. Hence, even though cell phone chargers are normally not considered a major use of electrical power, they have just as much potential to waste energy as a larger appliance, such as an answering machine or a computer monitor.

Conclusion

Our findings prove that, although cell phones are slightly worse in terms of energy usage than landlines, they also have other advantages which may outweigh this, most notably portability and ease of infrastructure implementation. We have also shown that landline networks, which used to be extremely efficient due to the very low quantities of power transmitted over conventional phone lines, have largely lost this advantage due to cordless phones, which require batteries, rechargers, an antenna, and a power supply from mains current in much the same manner that cell phones do. And both cell phone and cordless phone chargers, although they use very small quantities of power in comparison to most other appliances, should be a prime target for reducing energy waste, as they use a very large fraction of their normal power supply even when not in use.

Bibliography

Andræ, A. S., Mölle, P., Anderson, J., & Liu, J. (2004, October). Uncertainty Estimation by Monte Carlo Simulation Applied to Life Cycle Inventory of Cordless Phones and Microscale Metallization Processes. Retrieved February 7, 2009, from IEEE: http://ieeexplore.ieee.org/ielx5/6104/30320/01393085.pdf?arnumber=1393085

CTIA. (2008). Annualized Wirless Industry Survey Results – June 1985 to June 2008. Retrieved February 7, 2009, from CTIA- The Wireless Association: http://files.ctia.org/pdf/CTIA_Survey_Mid_Year_2008_Graphics.pdf

EIA. (2009, January 15). Net Generation by Energy Source: Total (All Sectors). Retrieved February 8, 2009, from Energy Information Administration: http://www.eia.doe.gov/cneaf/electricity/epm/table1_1.html

EIA. (2009, January 15). Petroleum Liquids: Consumption for Electricity Generation by Sector. Retrieved February 7, 2009, from Energy Information Administration: http://www.eia.doe.gov/cneaf/electricity/epm/table2_2_a.html

FCC. (2008, June 10). Statistics of Communications. Retrieved February 7, 2009, from Federal Communications Commission: http://hraunfoss.fcc.gov/edocs_public/attachmatch/DOC-282813A1.pdf

Lawrence Berkeley National Laboratory. (n.d.). Standby Power Summary Table. Retrieved February 7, 2009, from Standby Power: http://standby.lbl.gov/summary-table.html

Moore, D. W. (2004, December 17). Sweet Dreams Go With a Good Night’s Sleep. Retrieved February 8, 2009, from Gallup: http://www.gallup.com/poll/14380/Sweet-Dreams-Good-Nights-Sleep.aspx

Nicolaescu, I. V., & Hoffman, W. F. (2001). Energy Consumption of Cellular Telephones. Retrieved February 8, 2009, from IEEE: http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=924515&isnumber=19985

Nokia. (2005, April). Life Cycle Environmental Issues of Mobile Phones. Retrieved February 6, 2009, from The European Commission: http://ec.europa.eu/environment/ipp/pdf/nokia_mobile_05_04.pdf

Roth, K. W., & McKenney, K. (2007, January). Energy Consumption by Consumer Electronics in U.S. Residences. Retrieved February 6, 2009, from Consumer Electronics Association: http://www.ce.org/pdf/Energy%20Consumption%20by%20CE%20in%20U.S.%20Residences%20(January%202007).pdf

Sanchez, M., Webber, C. A., Brown, R. E., & Homan, G. K. (2007, March 23). 2007 Status Report: Savings Estimates for the ENERGY STAR® Voluntary Labeling Program. Retrieved February 7, 2009, from Lawrence Berkeley National Laboratory: http://enduse.lbl.gov/info/LBNL-56380(2007).pdf

Skerlos, S. J., Seliger, G., & al., e. (2003, May 22). Economic and Environmental Characteristics of Global Cellular Telephone Remanufacturing. Retrieved February 7, 2009, from IEEE: http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1208055&isnumber=27162

UCSD. (2008, November 26). UC San Diego Reports New Record for Wireless Base Station Power Amplifiers. Retrieved February 7, 2009, from UCSD Jacobs School of Engineering: http://www.jacobsschool.ucsd.edu/news/news_releases/release.sfe?id=799

US Census Bureau. (2008). Cellular Telecommunications Industry: 1990 to 2007. Retrieved February 7, 2009, from The 2009 Statistical Abstract: http://www.census.gov/compendia/statab/tables/09s1112.pdf

US Census Bureau. (2008). Population: National Estimates and Projections. Retrieved February 6, 2009, from 2009 Statistical Abstract: http://www.census.gov/compendia/statab/cats/population/national_estimates_and_projections.html

Appendix 1: Megajoules to Barrels of Oil

In the United States in 2007, a total of 87.005 million barrels of petroleum liquids were used for the production of electricity (EIA, 2009). Using this oil, US power plants produced a total of 49.956 TWh, or 179.8416 PJ, of electrical power (EIA, 2009). Dividing out, this equates to 0.48378 MBOE (million barrels of oil equivalent) per PJ of electricity, or 2,067 MJ of electricity per barrel of oil. Since pseudo-US power plants are likely to be similar in efficiency to US power plants, we can safely assume this conversion rate for the pseudo-US as well.

Appendix 2: Variables and Parameters

Variables Description:

  • A1: Starting point for logistic growth curve
  • A2: End point for logistic curve
  • x0: Midpoint year for logistic curve
  • dx: Growth rate for logistic curve
  • p: National population
  • I(c): Total power consumed by a single new cell phone over its lifetime3
  • R(c): Total power consumed by a single recycled cell phone over its lifetime
  • E(c): Power consumed by a single cell phone over its lifetime excluding manufacture
  • r: Power required to recycle a single cell phone
  • cp: Cell phones per capita
  • ct: Cell phone turnover rate
  • c: Total number of cell phones
  • I(c): Total power consumed by production and use of all cell phones annually
  • E(ci) Total power consumed by the cell phone infrastructure annually
  • t Number of cell phone towers per 1,000 people
  • E(t): Power used by a single cell phone tower annually
  • lp: Landlines per capita
  • l: Total number of landlines
  • I(l): Total power consumed by the production and use of all landline phones annually
  • w: Total number of cordless phones
  • E(w) Annual power consumption of a single cordless phone
  • wt: Cordless phone turnover rate
  • wr: Number of replacement cordless phones
  • ws: Number of cordless phones sold annually
  • M(c): Power consumption to fully manufacture and ship a single cell phone
  • M(w): Power consumption to fully manufacture and ship a single cordless phone
  • P(c): Electricity used in final production of a single cell phone
  • P(w): Electricity used in final production a single cordless phone
  • α: Hours the phone is in the charger already charged
  • pα: Power used per hour when the phone is charged but inserted
  • β: Hours the charger is empty
  • pβ: Power consumed by the empty charger
  • γ: Hours the phone spends actually charging
  • d: Number of devices that are currently in use in the US
  • Ewid: Power that the device uses while idle
  • Tid: Time per year that the average device spends idle
  • Ewod: Power that the device uses while ‘off’
  • Tod: Time per year that the average device spends ‘off’

1  See Appendix 1 for conversion from MJ to barrels of oil.

2 Data from Roth & McKenney, 2007

3 Note that I() includes all power required (inclusive), while E() is only the power drawn during use(exclusive).

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