Energy and the Cell Phone: A Model of the Next Fifty Years

Transcription

1 Energy and the Cell Phone: A Model of the Next Fifty Years I. Introduction In our model we consider the energy effects of mobile phones in America. We forecast the approach of mobile phone saturation and predict the total cell phone population in accordance with the increase in human population. Additionally, our model estimates the consequential decline of landlines and the change in energy costs to develop a picture of phone communication use in relation to time. This allows a study of energy use in a wireless-only America and the transition to that state. An extension of this study considers the most energy efficient method of implementing and maintaining phone service in a country comparable to the U.S., but lacking a communication infrastructure. This application considers the energy spent while a cell phone s Lithium-ion Polymer battery is charging and the unnecessary energy used by idle chargers in comparison with the Nickel-based batteries used in cordless telephones and unnecessary energy used while cordless phones are attached to their bases and not charging. These energy costs are considered in the simulated nation over the first fifty years of development. We also take a brief look at energy wasted by other electronic devices in standby mode. II. Description of Model Population growth is a fundamental contributor to the number of cell phones in America at a given time. Thus, modeling population growth in America is foundational for a model of mobile phone increase over time. Our population growth model is based on the U.S. Census Bureau s dicentennial census data, as well as their population projections. We use a least-squares approximation to develop a quadratic equation that accurately describes their data. Although logistic equations are most commonly used to describe population, our narrow focus on the first half of the twenty-first century validates using a quadratic population model. Fifty years is a short span of time in relation to the development of the human population, thus a quadratic graph accurately represents the growth of population from 2009 to A sigmoid, or logistic, curve accurately describes the increased use of cell phones from the late nineties until today. This so-called S curve initially increases slowly as cell phone technology begins developing, then more dramatically until finally slowing down as cell phones have saturated the population. This logistic description of cell phone growth in the U.S. uses historical wireless phone penetration data available from the Federal Communications Commission (FCC) to predict future growth. That is, we use these data to model a functional relationship between the ratio of total cell phones per human population and time.

2 To do so, a system of three logistic equations must be developed from three known cell phone saturations and their respective years. This system is used to solve for three important constants that describe the curve: M, k, and t 0. Here M represents the largest stable ratio of cell phones to population, k represents a growth constant, and t 0 represents the time at the inflection point of the S curve. Combining this functional description and accurate population predictions generates a model of cell phone growth in the U.S. Similarly, we can model the decline of traditional telephone lines. Instead of another logistic equation, we use a quadratic function defined in terms of the ratio of landlines to population. The logistic equation is not necessary because we do not need a bound at which the landline phones have reached saturation as they are decreasing to zero. The data for this model comes again from the FCC s historical data. This quadratic function clearly forecasts the time at which landlines are completely replaced, while maintaining a fit with known ratios of recent years. We use the least squares method again to derive this quadratic relationship. This declining ratio multiplied by the current population models the number of active landlines as a function of time. In both the cell phone and land line models, using a saturation ratio allows us to easily predict the number of cell phones or land lines in America during a specific year. Having developed equations that describe mobile phone growth and landline decline, we turn our attention to energy consumption. Modern cell phones are powered by either a Lithium-ion or a Lithium-ion Polymer battery. (Buchmann) An average of the top twenty bestselling cell phones on Amazon.com shows that these prevalent batteries have a battery life of 5 hours of talk time and 346 hours of idle time, as well as a charge time of three hours. A study by Berkeley Labs shows that Lithium-ion Polymer battery chargers draw approximately five watts when charging, one watt while plugged in but no longer charging (standby), and 100mW when the charger is plugged in, but no cell phone is attached. (Rosen and Alan) To utilize these numbers we use least-squares to establish a functional relationship between the number of cell phones in the nation and the number of minutes they are in use. Recall that our number of cell phones in the nation is a function of the year. Assuming that everyone charges their phone overnight (eight hours), we now can describe on average the amount of time each cell charger spends charging the phone, on standby (attached but not charging), and unattached to a cell phone. We then make the reasonable assumption that everyone leaves his or her charger plugged in for the remaining 16 hours of the day, but removes his or her cell phone from the charger. With these time frames we describe the average battery depletion as a percent for each cell phone in a day.

3 From that we model yearly energy spent charging and energy wasted (on standby and unattached to a cell phone) as a function of the year. That is, our function is in terms of charging time, standby time, and unattached time, which are defined in terms of total number of cell phones for a given year. Cell phone chargers are not the only source of energy consumption due to the rise in mobile phone popularity. Cell phones require transmitters and receivers to enable mobile communication. This equipment on cell phone towers also plays a major role in the energy footprint of mobile phones, because they draw more energy per unit than cell phone chargers. The term cell sites is a more commonly used term for the location of the transmitters and receivers for cell phones. Each site contains a tower structure with three sets of receivers and transmitters. Each set has one transmitter and two receivers. The receivers amplify the incoming signal, sending it to the base structure for processing and amplification for transmission. The amplification from the receivers takes little power (a max of 12 watt-hours), while the amplification by the transmitters takes significantly more power (a max of 200 watt-hours) (Narda East). Transmitters and receivers are, by nature, dependent upon the population of people owning mobile phones. So, a linear relationship between the two is an appropriate model. This linear relationship is developed using the least-squares method on extensive data from CTIA-The Wireless Association and the FCC. (CTIA-The Wireless Association) This relationship, along with the energy used by each transmitter, allows us to estimate the amount of energy used by cell phone towers in a given year. Considering this, with the energy needs of cell phone chargers finally gives us a comprehensive model of the energy utilized and energy wasted in a specified year.

4 Turning our attention to household phones, we assume that every household phone is a cordless phone. This is a reasonable assumption to make because cordless phones are very common in American households. Cordless phones use Nickel-based batteries (Rosen and Alan) which, according to the top twenty bestselling cordless phones on Amazon.com, have a battery life of approximately 11.5 hours in use and require seven hours to charge. Again we establish a functional relationship between the number of cordless phones in the nation and the number of minutes they are in use based on data from the FCC. Assuming that while not in use, these phones are attached to their base unit, we describe the amount of time spent actually charging these cordless phones along with the remaining time on standby as a function of total landline minutes. Using this function in tandem with the power required to charge a cordless phone (3.6W) and the power required for standby (2.6W) from Berkeley Labs, we develop an equation modeling both energy spent charging cordless phones and energy wasted on standby as a function of the year. (Rosen and Alan). In order to estimate the total energy usage of the entire landline system, we need to know the energy used by the landline central office switch stations. These switches service landline access lines which sort and redirect incoming and outgoing calls. Using current data from the FCC, we were able to model the decline in access lines as a function of the number of landline telephones using least-squares. With this equation, we were able to approximate the number of access lines in any given year. To simplify the model of energy usage, we assumed that all switches are Nortel DMS-100, because these are the most popular switches on the market. Knowing that a single DMS-100 can service 1000 access lines and operates at kw, we determine the number of DMS-100s and therefore the amount of power used by the landline infrastructure for each year. (United States Department

5 of Agriculture) Combining this with the energy used by cordless phones gives us a complete energy estimate for a landline telephone system. Now we have a function that describes the yearly energy use and waste of cell phones, as well as a function describing the yearly energy utilization and waste of landlines. Comparing the results from these models forecasts U.S. energy need and energy waste during the transition from landlines to a wireless nation. This model continues to describe the energy needs due to cell phones after landlines have been completely replaced by mobile phones. Considering a nation similar to the current U.S. without a telephone system in place, we utilize our previous model. Our results from the U.S. study show that cell phones and their transmitting equipment are more efficient than the system based on landlines. It is significant to mention that cell phones still currently run through some intermediate switches between towers. However, as landlines also run through the same intermediate switches, it is reasonable only to evaluate the differences in these two transmissions, i.e. the towers on the ends of cell phone communication and the switches on the ends of the landline communication. Because cell phones are more energy efficient and use less physical infrastructure we propose that a mobile phones system is best for the theoretical nation. To model the implementation of a mobile telecommunications system, we assume that the population growth of this pseudo America matches that of the real. The cell phone saturation will still follow a sigmoid curve, but in this case the pervasiveness is near zero at 2008; thus we develop a new logistic curve. To do so, we must first assume that the upper limit of cell phone saturation in this nation mirrors that of the U.S. Additionally, we must consider the length of time in which a telecommunications infrastructure can be developed. This period of time will be shorter than that of the US because the technology is already developed, and because they are only implementing one system of communication. Based on those assumptions and on the short time in which an interstate system was developed in the U.S., based on similarly significant need and prior lack of infrastructure, we assume that this nation can be fully saturated in nearly eight years. That is, within four years the infrastructure growth will begin to slow. This is reasonable as the current U.S. becomes saturated in nearly 15 years with effective telephone communication already in place.

6 Now we can build a system of equations to solve for the logistic curve that describes mobile phone saturation in our developing nation. Combining this curve with population estimates results in a forecast of the number of cell phones in this nation as a function of time. Our previously developed models of energy in relation to cell phone quantity remain the same. Thus, we use these in the new context of our developing nation s cell phone saturation to project the energy use and energy waste of this nation over the next 50 years. III. Results

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9 Real United States Year Population Number of Cells Number of Land Lines Number of Cell Cites Number of Switches ,610, ,609, ,526, , , ,605, ,567,286 11,583, ,405 6, ,302, ,074, , ,702, ,594, , ,803, ,753, , ,607, ,631, ,626 0 Year Waste Energy (kwh) Waste Energy (BOE) Energy (kwh) Energy (BOE) ,691,457,329 1,583, ,513, , ,297,423,670 1,939,661 1,176,775, , ,624,362,987 2,131,978 1,291,838, , ,941,947,590 2,318,793 1,403,608, , ,265,579,710 2,509,165 1,517,506, , ,596,035,491 2,703,550 1,633,806, ,063

10 Year Total Land Waste Energy (kwh) Total Land Waste Energy (BOE) Total Land Energy (kwh) Total Land Energy (BOE) ,286,408,720 6,639,064 3,268,951,991 1,922, ,652, , ,824, , Pseudo United States Year Population Number of Cell Phones Number of Cell Sites ,610,880 9,527,690 9, ,605, ,338, , ,302, ,170, , ,702, ,599, , ,803, ,753, , ,607, ,631, ,626 Energy (BOE) Waste Energy (kwh) Waste Energy (BOE) Year Energy (kwh) ,303,784 56,649 32,093,523 18, ,297,602,695 1,939,766 1,186,831, , ,604,199,685 2,120,117 1,297,423, , ,916,375,537 2,303,750 1,410,028, , ,235,317,347 2,491,363 1,525,073, , ,561,024,938 2,682,956 1,642,559, ,211 IV. Conclusions Our model depicts the total energy used in the U.S. by cell phone chargers and mobile phone infrastructure as being significantly less than the energy used by cordless phones and landline infrastructure. We predict that landlines will be completely replaced by cell phones in approximately the year During the transition period, cordless phone growth declines sharply, while cell phone saturation increases logistically. During most of the transition period, we predict that there are over twice as many cell phones as land lines, but land lines still use nearly five times the amount of energy of all national cell phones. After landlines have become obsolete, cell phones grow with the population. Our model predicted that cell phone saturation would cap at a

11 ratio of approximately This model predicts that the U.S. will waste more than 540,000 barrels of oil due to wasteful cell phone charging practices in However, we forecast that cordless phones will waste over 2,000,000 barrels of oil in 2009 alone; also, fifty years from now cell phones will still be consuming only one-fifth of the energy cordless phones consume in the year Based on these results, it is clear that a cell phone system is a more energy efficient telecommunications system. For the supposed pseudo U.S., the optimal phone system implementation is a mobile phone system. This is clear from the energy usage depicted in our first model. Also, a mobile phone system does not require phone wires spanning the nation. Instead, transmission and reception towers can be built much faster. Business workplaces often use a PBX system of wire-line phone extensions. This could still be supported from a wireless system if the workplace had transmission and reception capabilities that routed calls to and from desk phones. Unfortunately, cell phone waste is not nearly as concerning as waste from other consumer electronics. Cell phone chargers draw approximately 1W and 5W of power when on standby, but a cable box draws nearly 12W on standby. A television uses approximately 4W while on standby, a VCR uses 5.6W, and a compact stereo uses almost 10.6W. Estimates by Berkeley labs predict 5.4 TWh lost to televisions, and nearly 5TWh to VCR and compact stereos each. Thus it is clear that cell phones are not our most significant source of energy waste. (Alan, Meier; Huber, Wolfgang) Although the energy wasted by a single cell phone charger in one year is seemingly insignificant, when considering the 300 million plus population of the pseudo U.S. this waste is outstanding. We predict that the pseudo U.S. wastes nearly 700,000 barrels of oil in 2020 when this nation s cellular infrastructure has been developed in large part. This nation begins with very little cell phone saturation, and thus only uses approximately 57,000 barrels of oil (with almost 19,000 of that wasted. Over the next fifty years this increases to almost 2.7 million barrels of oil consumed and just fewer than 1 million barrels of that wasted. Thus it is easy to see that unplugging your cell phone charger really could make a difference.

12 Works Cited Amazon.com. Amazon.com Cell Phones & Service Best Sellers < Amazon.com Cordless Telephones < Telephones-Office-Electronics/b?ie=UTF8&node=172614>. Buchmann, Isidor. Battery University < CTIA-The Wireless Association. CTIA Survey Mid-year Washington, DC: CTIA, Federal Communications Commission. Trends in Telephone Service. Washington, D.C.: Federal Communications Commission Information Center, Meier, Alan K and Benoit LeBot. One Watt Initiative: A Global Effort to Reduce Leaking Electricity. Berkeley, CA: Lawrence Berkeley National Laboratory, Narda East. Narda East Tower Top Amplifiers. Product Description. HAUPPAUGE, NY: Narda East, "Nortel Products." DMS-100/200 Local Switching Systems. 7 February 2009 < d= &prod_id=8789&locale=en-us>. Rogers, Jack. "Kagan: U.S. Cell Phone Saturation May Spur Mobile Ad Rush." 27 August Media Post. 7 February 2009 < Rosen, Karen and Meier Alan. "Energy Use of Consumer Electronics in the US at the End of the 20th Century." Berkely Lab Environmental Energy Technologies Division < Thorne, Jennifer and Margaret Suozzo. "Leaking Electricity: Standby and Off-Mode Power Consumption in Consumer Electronics and Household Appliances." February American Council for Energy- Efficient Economy. 7 February 2009 < United States Department of Agriculture. "Bulliten 1751E-302." April February 2009 < US Census Bureau. US Census Bureau <