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Design for the Environment/Flashlights

This page is part of the Design for the Environment course

Flashlights are portable, hand held light sources. The company Urban Survival Tools supplies flashlights in their survival kits to be used as emergency light sources.

The three different flashlight design types are compared to determine the most environmentally friendly and economically viable flashlight design type. The three different flashlight design types are: non-rechargeable, or primary battery powered flashlight, dyno torch, and linear generator with supercapacitor flashlight.

A flashlight is essentially an encased power supply which powers a light source. Each of the design types use a Polyethylene casing and white light LED. Therefore, the analysis of the different design types focus on the different power sources of each design.

The non-rechargeable battery powered flashlight uses alkaline manganese battery, Duracell type AA batteries.

The dyno torch converts mechanical energy applied by the user’s hand to electrical energy which powers the light. The dyno torch alternative is hand powered and does not require the use of batteries. The dyno torch is very versatile and reliable and is suitable for emergency conditions.

Linear generator with supercapacitor flashlight is powered by several supercapacitors accompanied by a charging unit. Electric double layer capacitors, commonly known as supercapacitors, are the next generation of capacitors. The electric power creation is accomplished by electromagnetic induction. In the flashlight handle there is a tubular wire coil with a permanent magnet that translates back and forth inducing a current through the wire to be stored in the super capacitor.

The three different flashlights are analyzed to determine which flashlight has the best balance of functionality, environmental impact and economics.

Based on the analysis, it is recommended that Urban Survival Tools use the linear generator with supercapacitor flashlight. The linear generator with supercapacitor flashlight Scores highest on the streamlined life cycle assessment, how comparatively low harmful emissions than the other alternatives and is only slightly more expensive.

Project Information
Section 1 Group A21 Luke Jasudavicius (LJasudavicius) Oxana Kosorukova (Oxana.kosorukova) Sonu Chhibber (Mechysonu) Stephan Kennedy (SKennedy)

Non-rechargeable alkaline manganese batteries
Functional Analysis: General flashlight consumes energy from two alkaline batteries. On average, two Duracell batteries type AA should be replaced every 36 days. These batteries are defined as non-hazardous waste by the Federal Government (US) and can be safely disposed into trash. Recycle of non-rechargeable batteries is somewhat rare and performed during the steel-making process.

Economic Input-Output Life Cycle Assessment: The EIO-LCA used to analyze the non-rechargeable battery powered flashlights provided the following results: Power generation and supply sector, resulted from batteries pre-production and production stages, produce a largest effect on global warming potential. Point air, from factory operation, and non-point air, from truck transportation, plays the most important role in toxic air emissions. Land releases occupy 1630kg from all sectors. Particularly, important pollution metal such as zinc. Coal is the most consumable product for providing energy to manufacturing facilities.

Streamlined Life Cycle Assessment: The qualitative streamlined LCA used to analyze the non-rechargeable battery powered flashlights provided the following results: Overall matrix rating was calculated as 56. Low matrix ratings were given at pre-production and production stages for solid, liquid and gaseous residues, at usage stage for material selection and at disposal stage for solid residues. High matrix ratings were awarded at batteries transportation stage for liquid residues and at usage stage for energy use, solid, liquid and gaseous residues.

Cost Analysis: Total materials cost required for one battery manufacturing is ¢52. Pack of 144 Duracell alkaline batteries, type AA, costs $87.67 with $0.609 for one battery. No cost is required during usage or maintenance. Disposal cost of about 26 drums with alkaline batteries is $5,200. Recycling cost of about 26 drums is $15,600.

Societal Analysis: Primary batteries can discharge at the urgently needed situations and cannot be recharged but replaced only. Truck transportation of batteries releases noise and toxic emissions into the air, contributing to the smog and respiratory problems.

Dyno torch Flashlight
Functional Analysis: The dyno torch is hand powered and does not require the use of batteries. It utilizes more plastic than any other alternative and therefore more environmental impacts associated with the manufacturing and pre-manufacturing of plastic.

Economic Input-Output Life Cycle Assessment: The EIO-LCA used to analyse the dyno torch provided the following results: Large amounts of green houses gases are release in the pre-manufacturing of plastic from the oil extraction and petroleum refinery sectors. Also large amounts green house gases are released from premanufacturing metals from the steel mill sector. A tremendous amount of energy is consumed in the oil extraction and petroleum refinery sectors. the EIOLCA also suggested large Liquid residues are released in the petroleum refinery sectors and large amounts of solid waste in the steel mills sector.

Streamlined Life Cycle Assessment: The qualitative streamlined LCA used to analyze the dyno torch the following results: The stages of life cycle of the dyno torch that causes the most emission and scored the lowest on the SLCA is the pre-manufacturing and manufacturing stage. The usage of virgin petroleum, virgin steel and the significant release of land and water waste contribute such a low SLCA score for manufacturing and pre-manufacturing stage. The emission in the transportation, usage and disposal phase are small in comparison.

Cost Analysis: The unit price to produce and ship one dyno torch flashlight is 95 cents per flashlight.

Societal Analysis: Dyno torch is reliable and suitable for any situation especially emergency ones because of its 'unlimited' power power supply. however the dyno torch must constantly be pressed to generate power and therefore wrist injuries may become a hazard.

Linear generator with supercapacitor flashlight
Functional Analysis: The charging unit will compose of a kinetic energy generator built into the flashlight, which will charge the supercapacitors. Supercapacitors offer many advantages over conventional energy storage devices. They have a very high number of charge-discharge cycles (in the order of millions rather than 200-1000 cycles of a conventional rechargeable battery). For the application of the flashlight, the charge rate may no be consistent; this is one great advantage of the supercapacitor. It can be charged at any rate without degradation, unlike battery that requires a slow constant charge. The energy density and efficiency of the supercapacitor are also both great advantages allowing us to store a lot of energy with little waste. According to ITS (Institute of Transportation Studies, Davis, CA) test results, the specific power of electric double-layer capacitors can exceed 6kW/kg at 95% efficiency orders of magnitude higher that that of battery or conventional capacitors.

Economic Input-Output Life Cycle Assessment: The EIO-LCA used to analyse the linear generator with supercapacitor flashlight battery powered flashlights provided the following results: The power generation and supply create the most greenhouse gas emissions in supercapasitor manufacturing. The largest amount of energy is consumed by the power generation and supply. Ontario's electricity comes largely from coal fueled plants. This accounts for the 1.78 TJ of coal energy used by the sector. A significant amount of energy is also used in the provisioning of the material required for the supercapacitor and generator. The coal and metal mining and processing industries use a large amount of natural gas. The iron and steel mills create the largest amount of toxic releases. It consists mostly of water and land release. The releases come from all the impurities that exist in the iron ore that are removed in the milling process. Sulfur, phosphorous, and excess carbon are the major residues from the milling process.

Streamlined Life Cycle Assessment: The qualitative streamlined LCA used to analyze the non-rechargeable battery powered flashlights provided the following results: The linear generator with supercapacitor alternative has received a streamlined LCA score of 77. All categories given score of four during the entire usage stage of the linear generator because no material is emitted and negligible energy is consumed by the user’s hand. The supercapacitor uses a relatively large amount of activated charcoal compared to its total size. The production of activated charcoal consists firstly of mining the coal, followed by carbonization and oxidation of the coal at very high temperature. This is done to create the large porosity of the material that results in the high energy storage density of the material. This is an energy intensive process. Thus, lows scores are given for the pre-production section.

Cost Analysis: The assembly and the sales of the product would require direct cost as well as resulting indirect costs that may be subject to not only the manufacturing company but other sectors as well. Since a supercapacitor can withstand such high number of charge/discharge cycle and that the flashlight is intended to be used only on occasions, the user will most likely never have any additional cost. Municipal waste disposal for Toronto cost $50.75 per tonne as of 2000. The flashlight will weight approximately 350g thus costing $17.17 per 1000 flashlights discarded. To minimize environmental impact, the flashlight components should be recycled or resold.

Societal Analysis: The supercapacitor is more environmentally friendly than conventional capacitors for several reasons. The smaller size of the supercapacitor allows for less material to be used. The lack of electrochemical reactions reduce eliminate all hazardous waste in the disposal life stage. The supercapacitor is also completely RoHS compliant. The RoHS (Restriction of Hazardous Substances) is a directive to restrict the use of six hazardous commonly used materials in the electronic manufacturing industry. The supercapacitor industry is greatly back by many “green electricity” plans such as the GEL (Green Electricity Initiative).

Recommendation
It is recommended that Urban Survival Tools use the linear generator with supercapacitor flashlight. In the Streamlined LCA comparison, the total scores are as follows: non-rechargeable battery powered flashlight - 56, dyno torch - 72, and linear generator with supercapacitor flashlight - 77. The linear generator with supercapacitor flashlight scored the highest, only slightly higher than the dyno torch mostly due to the additional metals required for the dyno torch. Using EIO-LCA the total global warming potential of each design was found to be: non-rechargeable battery powered flashlight - 582 MTCO2E, dyno torch - 2030 MTCO2E, the linear generator with supercapacitor flashlight - 568 MTCO2E. Using EIO-LCA the total toxic releases of each design was found to be: non-rechargeable battery powered flashlight - 1940 kg, dyno torch - 2150 kg, the linear generator with supercapacitor flashlight - 1950 kg. The linear generator with supercapacitor flashlight has the lowest global warming potential and the second lowest toxic releases, only 10 kg more than the non-rechargeable battery powered flashlight.The linear generator with supercapacitor flashlight only requires to be shaken periodically to be recharged and has a lower mechanical input requirement than the dyno torch. This flashlight has the best functionally for its purpose and it also has the lowest environmental impact. However, it is slightly more expensive. The final cost of a linear generator with supercapacitor flashlight is $3.33 USD, compared to $0.95 for the dyno torch which is the product the current flashlight used in Urban Survival Tools survival kits. But, it is felt that all of the benefits of the linear generator with supercapacitor flashlight outweigh its additional monetary costs.

Non-rechargeable alkaline manganese batteries
Alkaline batteries produce an output voltage of 1.5 Volts and volumetric energy density of 320 Watt-Hours/Litre. It is sufficient for a flashlight to be operated for 6 hours without intermission. These batteries cannot be reused or recharged and therefore must be disposed and replaced by the new ones. There are three active components inside an alkaline manganese battery cell: Anode - contains high purity zinc powder, manufactured to ensure correct particle size and chemical impurity. Cathode – contains powdered manganese dioxide. It is made synthetically by electrolytic process. Graphite is used frequently as an additive to improve electrical conductivity. Electrolyte – alkaline. It contains concentrated aqueous solution of potassium hydroxide. To prevent corrosion of zinc, zinc oxide is added Upon discharge of a battery, the reduction of manganese dioxide leads to the zinc oxidation which is simplified in the following reaction: Zn + 2MnO2 -> ZnO + Mn2O3

The percentages of each composite inside a single battery :

Under test conditions, flashlight power source requires current of 3.9ohms for type AA primary batteries and have on average 6.2 actual service hours.

Metal shelves should be avoided as a storage place for batteries. Storage temperature for batteries has to be maintained between 10°C and 25°C. Relative humidity should not exceed 65%. In order to maximize battery’s shelf life, it should not be stored at the temperature above 25°C. Batteries should be removed from the equipment all the time when it won’t be used for several months. It will prevent possible damage. Replacement of all batteries should be done simultaneously. Mixing batteries, for example alkaline manganese with zinc-carbon should not be practiced as it causes voltage reversal. Recharge of non-rechargeable batteries should never be done, as it creates imbalance inside the cell that results into acid leakage or gassing and possible explosion.

The advantage of non-rechargeable battery is that it does not consume energy while being used. It is safe and easy to use and allowed to be disposed into trash.

The disadvantage of non-rechargeable battery is that it can discharge during unwilling moment without a chance of being recharged. It also produces hazardous wastes during pre-production and production life stages.

Dyno torch Flashlight
Dyno torch does not require the usage of batteries for power. Rather power is generated in the dyno torch by converting mechanical energy to electrical energy where the mechanical energy is produced from the user cyclically pressing down on the crank. Dyno torch is comprised of plastics and metals. The metallic components of the flashlight include copper wires, flywheel, magnet, magnet casing, resistor, spring, pin shafts and screws. The plastic (polyethylene) component of the dyno torch include crank internal, gear rack, internal gears, casing, LED light and lens. Unlike the battery operated or Faraday alternative, the dyno torch’s power source is not storage based (ex. battery or super capacitor).

The advantage of thee dyno torch is that it is hand powered and does not require the use of batteries. The dyno torch is very versatile and reliable and is suitable for emergency conditions.

The disadvantage of the dyno torch is that in order to continuously generate light in the LED like the battery powered alternative; the user must constantly press down on the crank cyclically which can be cumbersome. Another disadvantage is that Dyno torch utilizes more polyethylene (plastic) than the other alternatives as a result of usage of internal gears used to transfer power in the mechanism and therefore cause more emissions as a result of manufacturing process of plastic.

Linear generator with supercapacitor flashlight
Supercapacitors - electric double layer capacitors are the next generation of capacitors. The charging unit will compose of a more conventional kinetic energy generator built into the flashlight. The electric power creation is accomplished by electromagnetic induction. Tubular wire coil with a permanent magnet in a flashlight translates back and forth inducing a current through the wire. The signal is then rectified with a signal diode circuit to create a DC current. The electricity is to be stored in the supercapacitors. Supercapacitor is formed of two collector plates of a common material submersed in an electrolyte solution. The layers are physically separated by a very thin dielectric separator. It is the electrical property of the material known as the electrical double layer principle along with the dielectric separator that allows for the charge separation to occur. Most commonly, supercapacitors use activated charcoal to store the energy due to its porosity thus resulting in an extremely large surface area. Although it is an electrochemical device, there are no chemical reactions occurring to produce energy such as in a conventional battery. The energy is stored electrostatically electrolytic solution.

The advantage of supercapacitor is that it has a very high number of charge-discharge cycles (in the order of millions rather than 200-1000 cycles of a conventional rechargeable battery). For the application of the flashlight, the charge rate may no be consistent; this is one great advantage of the supercapacitor. It can be charged at any rate without degradation, unlike battery that requires a slow constant charge. The energy density and efficiency of the supercapacitor are also both great advantages allowing us to store a lot of energy with little waste. According to ITS (Institute of Transportation Studies, Davis, CA) test results, the specific power of electric double-layer capacitors can exceed 6kW/kg at 95% efficiency orders of magnitude higher that that of battery or conventional capacitors.

The disadvantage of the supercapacitor is that it cannot produce a voltage of more than 2-3 volts. Most electronics operate at low voltage thus solving the problem. In the case where higher potentials are needed, the problem can be circumvented by wiring supercapacitors in series circuits.

Details on Economic Input-Output Life Cycle Assessment
The EIOLCA for the alternatives may be viewed or downloaded

Non-rechargeable alkaline manganese batteries
Power generation and supply is the major sector of battery manufacturing that produces the largest effect, 176 MTCO2E, on global warming potential upon the release of toxic emissions into the air. It is done at the pre-production and production stage of a battery, when materials such as zinc, nickel, alkali, manganese, and carbon are extracted, supplied to the factory and transformed into the useful materials for the manufacturing field. Iron and steel mills, used for steel cans production of batteries, is a second largest sector with great influence on GWP. Truck transportation, caused 43.1MTCO2E of GWP with 42.4MTCO2E of carbon dioxide emmisions, is used for materials and batteries’ shipment, therefore cannot be ignored. When non-rechargeable batteries are used to create 1kWh of energy, the impact on global warming is comparable to driving 457km.

Total toxic releases to the air in primary battery manufacturing process are 18.24kg of emissions. Point air happens during making alkaline manganese dioxide acid from raw materials, steel cans and nickel plates. Non-point air releases produce 10.0 kg of toxic emissions due to the transportation of materials and batteries to the retail stores by trucks.

When non-rechargeable batteries are used to create 1kWh of energy, the impact on air pollution is comparable to driving 2,320km.

The impact on air acidification is comparable to driving 19,812km.

Manufacturing of batteries is an energy intensive process. Mainly, during power generation and supply sector since coal is needed for factory operation to perform paper processing, manganese dioxide formation, steel can punching. Extraction of materials and its supply to the facility consumes energy. Truck transportation of a battery requires fuel and therefore is an energy consuming process.

Dyno torch Flashlight
An custom product EIOLCA was created using the EIOLCA software with the following economic activity distribution $400, 000 for petroleum refinery sector, $400,000 for plastic manufacturing sector, $100,000 for iron and steel mill, $50 000 for steel manufacturing, $40 000 for ferrous manufacturing and finally $10 000 for copper manufacturing.

The phases that release the most emissions throughout the lifecycle of the dyno torch is the premanufacturing (oil extraction and petroleum refining) and manufacturing (plastic resin manufacturing) stage. The sectors that contribute most to green house gas emissions are the oil extraction and petroleum refinery sectors. The GWP (Global warming potential) that oil extraction and petroleum refinery sector release are 353 and 339 MTCO2E respectively. In addition petroleum refinery sector cause a great deal of CO2 emissions (351 MTCO2E) and oil extraction cause large CH4 emissions (282 MTCO2E) Also Large amounts of GWP and CO2 are release pre-manufacturing metal at steel mill sector (both released at 177 MTCO2E).

The largest amount of land and water wastes is produced in the pre-manufacturing stage. The steel mill sector accounts for most of solid and liquid waste releases at 41.1 and 61.6 kg respectively. The petroleum refinery sector that pre-manufactures petroleum to plastic is also a significant source of liquid waste (28.4 kg).

Large energy requirement for a sector indirectly corresponds to large toxic emissions required to generate that energy. The sector that consumes the most energy in the manufacturing of dyno torch is the petroleum refinery sector which requires 6.57 TJ which is significantly higher than the rest of the sectors. The plastic resin manufacturing sector also consumes large amount of energy (3.17 TJ). An interesting observation can be seen from the energy requirement required to manufacture an pre-manufacture dyno torch. It is observed that the main drawback of the dyno torch is that it utilize more plastic than the other alternative and from the EIO-LCA; premanufacturing and manufacturing plastic into product utilizes the most energy inefficient sector (aka petroleum refinery and plastic resin manufacturing).

Linear generator with supercapacitor flashlight
The power generation and supply create the most greenhouse gas emission. due to the energy requirements of the pre-production stage of the supercapacitor life cycle. The emissions from the power generation are mostly CO2 release from coal fueled power stations. In Ontario, there are five coal burning power plants that contribute to the total emissions. The Ontario Power Generation supplies 85% of all power in Ontario and has many initiative progresses that try to minimize the emissions which have led to a reduction of 41% of Nox emission from 1999 to 2004.

The motor and generator manufacturing emit a significant amount of toxic air release due to the amount of metal needed in the production. The energy required and processing of the metal produces a total of 29.4 kg of air release. About 83% of air releases are point. This relatively high percentage of air release is a good thing with regarded to the control and analysis of air emissions. Since the majority of air emissions are stack, they are thus known and can be managed with proper procedure. The iron and steel mills create the largest amount of release. It consists mostly of water and land release. The releases come from all the impurities that exist in the iron ore that are removed in the milling process. Sulfur, phosphorus, and excess carbon are the major residues from the milling process

The largest amount of energy is consumed by the power generation and supply. Ontario's electricity occurs largely from coal fueled plants. It accounts for the 1.78 TJ of coal energy used by the sector. Provisioning of the material required for the supercapacitor and generator uses a significant amount of. The coal and metal mining and processing industries use a large amount of natural gas. The iron ore must be smelted at very high temperature. It requires a large amount of energy taken most commonly from the burning of natural gas. 0.677TJ of energy is required from natural gas to produce the metal components of the flashlight power source. There is possibility to reduce the energy consumption by eliminating the need for metal. The generator casing along with the wire may be replaced with plastic and conductive polymers, although this may not be financially sound.

Non-rechargeable alkaline manganese batteries
Pre-production stage: Solid residues are left during extraction of zinc and nickel.

Product manufacturing stage: Alkaline manganese dioxide, an acid, is used for filling the battery. Paper, zinc, nickel and iron are used inside the specified battery and considered as the materials that cause substantial emissions of toxic, smog-producing or greenhouse gases into the environment. Matrix rating for solid, liquid and gaseous residues in this stage is defined as 1.

Distribution stage: No liquid residues during batteries transportation. Matrix rating for liquid residues sector is given as 4.

Usage stage: Non-rechargeable battery powered flashlight requires its batteries to be replaced periodically. Matrix score of 1 is given for material selection. Battery is a power source; it does not require any energy to operate. Under normal operating conditions battery does not release any solid, liquid and gaseous residues. Matrix rating for energy use, solid, liquid and gaseous residues is given as 4.

Disposal stage: Batteries contain many different solid materials which can not be easily separated. It scores 1 in solid residue. The batteries contain acid, which contribute to its low score in liquid residue.

Dyno torch Flashlight
Pre-production stage: A large amount of energy is consumed to refine virgin petroleum to plastics this SLCA score 1 is given. Refining petroleum to plastics cause large water waste while the usage of plastic is not minimized; a score given score of 1 and can be verified by referring to water emission of petroleum refinery sector in EIOLCA. Solid residues scored 3 due to the minimum usage of metal. Product Manufacturing stage: Manufacturing plastic into desired components produces liquid waste that has not been minimized. Score of 2 is given.

Distribution stage: The components of the dyno torch are small in size and volume. Transportation energy consumption is minimized. A Score of 3 is given.

Usage stage: No material is emitted and negligible energy is consumed from the user’s hand. All categories are given score of 4 during the entire usage stage of the dyno torch.

Disposal stage: The polyethylene components in the dyno torch are recyclable. A score of 4 would have been chosen, but since the dyno torch also contains different kinds of metal components, a conservative score of 3 was chosen instead for solid residue.

Linear generator with supercapacitor flashlight

Pre-production stage: Relatively large amount of activated charcoal is used in supercapacitors compared to its total size. The production of activated charcoal consists firstly of mining the coal, followed by Carbonization and oxidation of the coal at very high temperature.. This is an energy intensive process. Score of 0 is given for the energy use.

Product Manufacturing stage: Production of the components is rather simple and invasive. The material and energy inputs have been minimized as much as possible. The capacitors can use recycled metals as casing. The production of the components produce little residue since the production is in most part a simple assembly process. A score of three is given for this life stage

Distribution stage: The energy of distribution is greatly minimized due to the size of the product. This reduction in size, contributes to a high score in both material and energy. Very little packaging is required and transportation costs are reduced. The material residues are minimized.

Usage stage: No material is emitted and negligible energy is consumed by the user’s hand. Score of 4 is given.

Disposal stage: Components of the linear generator and supercapacitor are distinct and reversibly separable. The linear generator is composed of recyclable metal and rare earth magnet. The supercapacitor's casing is recyclable metal as well as the activated charcoal may be resold or reused since it use in the supercapacitor is not destructive. Activated charcoal is often resold to be used as a component in filters (i.e. charcoal filter).

Non-rechargeable alkaline manganese batteries
Direct Costs: Single alkaline battery weights 23g. Cost of the materials for one battery manufacturing is ¢52.

Supplier’s cost for 144 batteries pack costs $87.67 with $0.609 per battery. Battery does not require any operation costs upon the usage because it is power source and does not consume electricity or materials. There are no maintenance costs, since primary battery is replaced upon discharge only and the flashlight is used in an emergency kit, which means that it will be on rare occasions for the flashlight to be used. At the end of lifetime, batteries are disposed into trash. Disposal of about 26 drums with alkaline batteries costs $5,200. Rare recycling is done during the steel making process and occupies on average $15,600 for 26 drums.

Indirect Costs: Flashlight uses two alkaline batteries at a time. Assuming that a flashlight will be used 10 minutes per day, the user would have to replace two batteries every month.

Dyno torch Flashlight
Direct Costs: The manufacturing cost of the dyno torch includes the cost of pre-production the metal and plastic components of the dyno torch. The cost to run the manufacturing equipment, injection molding machine and extrusion machine used to form the plastic and metal into the dyno torch components (cranks, gears etc.) is also considered. The cost to produce one dyno torch flashlight in China is $0.95. The transportation cost from china to Canada is $9.40 per kg. The weight of each dyno torch is approximately 102.5 gram. Total transportation cost of one dyno torch is $0.9635/flashlight.

No cost at the usage stage as no batteries are required to power flashlight. The disposal cost in Toronto is $50.75 per ton. the cost to dispose of dyno torch is $5.73/1000flashlights.

Linear generator with supercapacitor flashlight
Direct cost: Total direct cost to manufacture one supercapacitor is $3.3259. Conventional capacitors, around 100μF, are sold for $2.29573 opposed to the 1F supercapacitor, sold, for $1.65.

Disposal costs are minimized due to the long life-cycle of the product. When the flashlight life-cycle does come to an end, most likely due to physical damage or lack of need, it will presumably be discarded in normal trash. The waste disposal cost will be incurred by the city. Municipal waste disposal for Toronto cost $50.75 per tonne as of 2000. The flashlight, weighting approximately 350g, costs $17.17 per 1000 flashlights. Flashlight components should be recycled or resold for minimized environmental effects.

Non-rechargeable alkaline manganese batteries
Non-rechargeable alkaline manganese batteries are safe and easy to use. However, discharge of batteries can happen at the unwanted moment. Recommendation for user is to have two extra batteries.

Truck transportation of batteries to the company and retail locations causes a lot of toxic emissions to the air. It causes smoke and may be the cause of respiratory problems.

Dyno torch Flashlight
The dyno torch has a positive affect on society as it is reliable and does not require the use of batteries. It helps users out of emergency situation such as being lost in the woods at night. The dyno torch is the ideal flashlight for emergency lighting situations. One downside that the dyno torch flashlight might have on society is that strain injuries may result in the wrist and arm from continuously pressing down on the crank.

Linear generator with supercapacitor flashlight
The supercapacitor is more environmentally friendly than conventional capacitors. The smaller size of the supercapacitor allows for less material to be used. The lack of electrochemical reactions reduce eliminate all hazardous waste in the disposal life stage. The supercapacitor is completely RoHS compliant. The RoHS (Restriction of Hazardous Substances) is a directive to restrict the use of six hazardous commonly used materials in the electronic manufacturing industry. The supercapacitor industry is greatly back by many “green electricity” plans such as the GEL (Green Electricity Initiative). The technology and efficiency of the supercapacitor is quickly advancing thanks to a large demand and will for more cheap and reliable eco-friendly products.

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Why Do I Like What I Like?
Mark di Suvero’s Bunyon’s Chess sculpture was definitely not a winning first impression. Walking toward the sculpture, from a distance it simply looked as if the artist hung a few logs together which made it difficult for me to appreciate. At a glance, usually bright colors and easy, flowing compositions are typical elements that catch my attention. So with this piece, it was the lack of color and smooth lines that initially turned me off.

When I began to research di Suvero I found a pattern among his works. I discovered that all of his sculptures were very architectural, often using steel or wood. His sculptures look as if they are colliding in a windstorm caught in a still photo. Yet it stands firmly in front of you, each part securely fastened. One of his other pieces, Che Faro Senza Eurydice, is a perfect example of that. The sculpture consists of multiple pieces of weathered wood strung together with rope. Although these are basic materials you could find on a beach, di Suvero has constructed those natural elements to push and pull against each other to look as if they defy gravity. Di Suvero quotes, “that's why I like to suspend elements from the beams of my works, so they can interact with the wind and other forces.”

Although di Suvero’s sculpture in the park didn’t instantly read as beautiful to me, after researching his thought process, now it does. Not only can I now appreciate the raw, basic materials di Suvero has thoughtfully structured to show movement and interesting spatial techniques, but it’s an admirable feat that he was able to assemble these massive logs and steel bars together and still create a beautiful work of art.

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Design for the Environment/Residential Heating and Cooling in Ontario

This page is part of the Design for the Environment course

Project Information
The purpose of this article is to explore alternative methods of residential heating and cooling that have not yet gained significant public presence or awareness, with the end goal of identifying the most advantageous alternative, with respect to function, environmental impacts (judged by EIOLCA and SLCA), cost and societal concerns.

Section 2 - Group B1

Yufei Man (manyufei)

Owen Moffitt (takata)

Steven Nadeau (nadeaust)

Ground Source Heating
Ground source heating/cooling utilizes thermal energy from the earth to heat or cool a house. Unlike the temperature of air which fluctuates throughout the seasons, the temperature slightly below ground is consistent year round. A geothermal system utilizes this phenomenon to control the temperature of the house. The system consists of three elements: an underground piping system, a heat pump and a distribution system for the house. During wintertime, the temperature below ground is warmer than in the house. This heat is absorbed by the fluid in the underground pipes which circulates to the house. The heat pump utilizes refrigerants which extract this energy and distributes it through the ventilation system of the house. During the summer, this process is reversed. The heat pump extracts the thermal energy from the house where it gets sent below ground. In this configuration, the earth acts as a heat sink. A ground source heating/cooling system only requires a small amount of electricity to power the heat pump which is why it is so efficient. Unlike traditional systems, the heat is not created through a combustion process but simply extracted from the ground.

Thermoelectric Solid State Heat Pump
A thermoelectric (TE) solid state heat pump operates based on the Peltier effect, in which electrical energy is converted to thermal energy. A thermoelectric module consists of a thermoelectric material, typically semiconductors such as Bismuth telluride (Bi2Te3), sandwiched between two ceramic plates joined with electrical interconnects. When a voltage is applied to the device, heat is transferred from one side to the other, typically against the temperature gradient. The direction of heat travel depends on the sign of the voltage, and thus the device is capable of providing both cooling and heating. The term “solid state” refers to the fact that the device has no moving parts, thus enabling it to run fairly quietly and requiring minimal maintenance.

TE heat pumps operate purely on electricity, so precise temperature control can be achieved as we can directly measure and control the current flow into the system. To date, TE solid state heat pumps are primarily used in cooling applications, whether it’s for electronic components that require specific constant temperatures, or portable coolers for personal use. Large scale applications however, in this case the heating and cooling of an entire residential house, are extremely rare or almost nonexistent, due to the potential cost and complexity of the overall system.

SLCA
The SLCA analysis yielded inconclusive results, as the differences between the scoring of the two alternatives was too low to warrant definitive assertions. Furthermore, the SLCA failed to signify the most marked difference between the technologies of all: energy use during process operation. This was represented by a single matrix value, which only contributed to a difference of 2 out of 100 in the gross SLCA score. From the perspective of the EIOLCA and cost analysis, this is an inexcusable oversight. For this reason, the SLCA score is an inappropriate means of comparison. What it did accomplish, however, was to establish the general differences between the alternatives, which were verified with greater rigour in the quantitative analyses.

EIOLCA
The EIOLCA produced much more quantitative and useful results, which proved to be highly illuminating. Refering to the EIOLCA data, it is definitively clear that the process operation phase dominates the environmental impact. For example, the process operation phase accounted for 87% of the total GHG emissions released throughout the life cycle for ground source heating, and a staggering 97% for TE heat pumps. The same trend can be noticed in terms of all environmental metrics in the EIOLCA. Comparing the environmental outputs of the two alternatives, we see a very marked difference. In terms of every environmental metric, TE heat pumps have approximately 6 times the impact of a geothermal system over a lifetime of 50 years. This discrepancy is so high that it is a significant, if not a deciding factor in our analysis.

Cost Analysis
The cost analysis reveals an identical trend. While the startup costs for geothermal systems are significantly higher, the variable cost of process operation is over 6 times higher for TE heat pumps. Taking the present value of money into account, the cumulative cost of a TE heat pump over the course of a 50 year lifetime becomes roughly 3 times greater than for a geothermal system over the same lifetime. This is still a hugely significant factor.

So with respect to every analysis thus far, geothermal systems have proven far superior. As the duration of system use extends beyond even half a decade – far below the total life of the system – geothermal emerges as victorious with respect to both cost and environmental impact, at a significant order of magnitude.

Societal Analysis
The only caveat to this otherwise flawless victory is the special societal considerations required for ground source heating. The comparatively high initial investments as well as the invasive installation procedure are significant barriers to overcome.

Conclusion
Ultimately, it is the users’ decisions to that decide whether or not this alternative spreads as a viable alternative to current heating and cooling methods. As a major stakeholder in the economic and environmental demands of its citizens, it is recommended that governments introduce adequate funding and programs to help accomplish this goal. If the initial investment can be made by a willing party, the overall impact for all stakeholders is significantly lower costs and environmental demand.

Ground Source Heating

Ground source heating takes advantage of free geothermal energy – it comes from a virtually infinite reservoir. Electricity input is only required to bring the geothermal energy to a usable temperature. As a result, the efficiency of the heat pump in this system is actually greater than 100%. For every joule of electricity inputted, more than one joule of heat is outputted due to the contribution of the ground heat. This is a highly effective use of cascade approach –use a low quality energy source input to yield a low quality energy source output, resulting in minimal waste in energy conversion. Based on this qualitative analysis alone, we can expect that the operating energy demand will be lower than for TE heat pumps. However, as mentioned previously, installation is invasive and we can expect the fixed costs (both economic and environmental) to be higher.

Thermoelectric Solid State Heat Pump

In contrast, a TE heat pump has only a single input; electricity – and you have to pay for every joule. This means system efficiency, while higher than natural gas heaters, is below 100%. Electrical energy is also a high quality energy source, so its use to yield a low quality energy output is not ideal. Since a TE heat pump functions as a standalone unit, however, fixed costs are anticipated to be lower, at the expense of a higher variable cost of operation.

Ground Source Heating

Geothermal systems require very little power to run during the use stage. For this reason, the primary polluting stages are the pre-manufacture and manufacturing phases. The piping used to gather the underground heat is made of HDPE. The extraction of the petroleum required to make these pipes is energy intensive and requires metal machinery which release large amounts of greenhouse gases and toxic emissions. The heat pump contains metallic parts such as steel and copper which emit many toxic emissions when they are extracted and smelted. Also, the installation of the piping requires digging large trenches to bury them. This process requires metallic machinery as well as large amounts of energy which cause large amounts of pollution, primarily in the form of GHG’s and toxic emissions.

However, once the system is in place, very little is required to make it function. A relatively small amount of electricity is needed to power the heat pump. This electric requirement is the only source of emissions for this stage. Over an assumed fifty year lifespan, the emissions of the geothermal system are lower than for a thermoelectric system across the board.

Thermoelectric Solid State Heat Pump

Thermoelectric solid state heat pumps do not require a significant amount of resources to produce. Therefore, the premanufacturing and manufacturing stages account for a very small portion of the total emissions and energy requirements. Not only are TE heat pumps relatively small compared to a geothermal system, but most of the constituent materials can obtained from either recycled sources, or as by products of other material extraction/refining processes. In terms of product distribution, most products are simply transported via trucks across North America, accounting for the small percentage of total emissions and energy requirements.

Naturally, with a lifespan of 25 years, the process operation stage occupies the vast majority of the product lifecycle. Since TE heat pumps require only electricity, a unit would require a significant amount in order to be able to heat/cool an entire household. This high demand for electricity would have to come from power plants, many of which burn fossil fuels. Over a period of two lifespans of 50 years, the high amounts of fossil fuels burned to generate the required power would result in enormous emissions and energy requirements, most notably the incredibly high greenhouse gas output, as power plants account for approximately 25% of the world’s total carbon dioxide emissions.

When the unit has reached the end of its life, it can simply be disposed of like any other household appliance. Being no bigger than a typical natural gas furnace, the user can simply drive the unit to a nearby waste disposal facility, where it is disposed of like any other old appliance. Such a common process does not have emissions or energy requirements that would be significantly higher than for other heating/cooling units such as geothermal or natural gas and air conditioning.

Compared to a geothermal system, a thermoelectric system definitely results in higher greenhouse gas/toxic air/conventional air pollutants emissions and total energy requirements over a period of 50 years.

SLCA (Streamlined Life Cycle Assessment)
Based on the totals alone, we see that the two alternatives score very comparably, at 61.5 and 64.5 out of 100, respectively. A 3% difference is not significant and does not warrant a judgment in favour of TE heat pumps. However, we can compare the SLCA values by subtotal to see where the differences and similarities lie.

Both alternatives perform very poorly in resource provisioning, due to the large number of extraction processes required to obtain the raw materials, particularly the variety of metals in thermoelectric devices, and in the case of ground source heating, the use of petroleum products for the pipes. TE heat pumps outperform ground source heating marginally in the production stage, due to the use of refrigerants in ground source heating that can evaporate and act as greenhouse gases. This happens again in the distribution and process implementation stage, due to the high energy cost associated with digging and laying the pipes that are specific to ground source heating. Ground source heating’s high efficiency allows it to outscore TE heat pumps in the process operation stage. In fact, it should be noted that it receives a perfect 20/20 score during this stage. This should be given special consideration, as the long life of heating and cooling systems make the process operation stage one of the most crucial factors on environmental demand. While purchasing and installation of each alternative may only require days or weeks, the process operation stage goes on for decades.

Ground Source Heating
The initial cost of a geothermal system is quite high ranging from $22,700 to $47,700. These costs include the digging of the trenches, the purchase of the heat pump and the upgrade to the ventilation system. The price varies depending on the size and location of the home. However, the operational cost is very low at about $1000 per year. This amounts to about 36% of a traditional natural gas system. Therefore, the money saved versus a traditional system allows the cost to be recuperated within 4 to 10 years, and thus in the long term, the purchase of a geothermal system can be profitable.

There are also other benefits to the installation of this system. Financial incentives can be obtained depending on the governmental regulations in the area of the house. Furthermore, the installation of a ground source heating/cooling system increases the value of the house since it has such high long term benefits.

Thermoelectric Solid State Heat Pump
Since there were no thermoelectric modules of such scale currently on the market, we had to estimate and extrapolate to determine a suitable price for a TE module to heat/cool an entire house. Given that typical natural gas furnaces range from 40,000Btu/h to 150,000Btu/h, we will use 90,000Btu/h as the average required output of a residential heating unit. 90,000Btu/h amounts to about 26,400W of power, which is required to flow across the heat pump. Based on a manufacturer quote of $12CAD for a 140W module, a TE module that outputs 26,400W of power will cost approximately $2,260CAD. Factoring in the cost of a heat sink and other miscellaneous components, we have decided on $2,400CAD as the average price of a unit.

The most efficient thermoelectric devices can achieve up to 17% Carnot efficiency. Houses built from 1946 to 2006 have an average annual gross thermal output requirement of 65GJ (18,000kWh), meaning that the total energy put into the system is near 106,000kWh. At current electricity rates, taken from Toronto Hydro Electric System electricity bill, of $0.056/kWh for first 2,100kWh, and $0.065/kWh for beyond that, we are looking at an annual cost of about $6,871(CAD) to heat/cool a home purely using TE heat pumps.

For a thermoelectric system, the initial cost of $2,400 may be seemingly low compared to that of a geothermal system. Over time, however, annual costs of $6,871 will accumulate, eventually becoming much more of a financial burden than would a geothermal system. In fact, it only takes five years for a geothermal system to become more economical overall than a thermoelectric system, as shown in the graph.

Societal Analysis
One significant concern that is not accurately captured by quantitative analysis is the effect on desirability of the two technologies from their vast difference in price and convenience. A thermoelectric system requires minimal capital investment and non invasive installation. A geothermal system, on the other hand, requires extensive investment and large scale renovation. This will cause resistance amongst some users, making widespread adoption of this technology more difficult. Economic and environmental savings can only be realized once the initial large scale investment has been made.


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User:Kylnso/studioproduction-dfvp200

LAST UPDATE - 4/23

STUDIO PRODUCTION
20 minute live production

CREW LIST
•	ANDRE - Director •	DREW - Talent / Script Writer •	SCHICK - Technical Director •	KAYLEN - Floor Director •	ERIN - CG / Editor •	SARA - Robo Cam •	BRITTANY - Teleprompter & Tape •	ANNA - Talent •	Terrence - Audio •	Sam & James - Lighting •	Bret - Communications •	Mario - Camera •	Jerry - Set design

PROPOSAL / TREATMENT
"AIS LIVE" will be a weekly, 20-minute studio production with the current news at AIS and featuring guests sharing their experiences and life at AIS.  The proposed host for the show is Dr. Drew Hisey, who has an established track record with us for doing student life specials. He will have various guest with new experiences and stories to share.  We will have the AIS man of the year Dan Frabrizio to come in and be interviewed. Also we have Anna, our lifestyle correspondent who will be showing us simple ways to save money in this time of economic crisis. Production costs would be minimal. The production will be done live-to-tape on Tuesday afternoons in Studio B with three cameras. Dr. Hisey indicates he would be willing to host the show for free! Our initial contract with Dr. Hisey would be for 12 shows.

PRODUCTION'S GOALS & PURPOSES

To present the current ongoing news at AIS, and give an outlook of everyday student and faculty life at AIS.

BREAKDOWN/SEGMENTS
(UPDATE 4/8) INTRO (0:30) Block #1 (5:30) - The News Commercial break - Infomercial  (1:20) Block #2 (5:30) - Talk with Correspondent Commercial break - Movie Trailer  (1:20) Block #3 (5:30) - Interview with Dan Fabrizio Commercial Break 3 - TBA  (1:20) "Well that's all, join us next week for..." (0:15) TAG (0:30 min)  About 21:45

SOUND ON TAPE
• ANDRE – Script writer • DREW - Talent / Script Writer / cam operator / editor • SCHICK – talent / script writer / lighting • KAYLEN – Talent / script writer / cam operator / editor • ERIN – talent / script writer / cam operator / lighting • SARA – talent / script writer / cam operator / lighting • BRITTANY – talent / script writer / lighting / boom • ANNA - Talent / Script Writer / lighting

SCHEDULE/CALENDAR
•	WEEK 1 TUES 7 - Concept meeting •	WEEK 2 SHOOT & EDIT SOTs •	WEEK 3 TUES 21 - Rehearsal for show •	WEEK 4 TUES 28 - Show & Production book due

EQUIPMENT LIST
- Panasonic DVX 100 / Tripod - Sony HVR-Z1U / Tripod - HVR Battery - CGP Battery - Power Strip - Extension Cord - Lowel VIP Kit - Gloves - Reflectors - Gels - A/C Power - Lav Mic - XLR Cable

title: User:Kylnso/studioproduction-dfvp200


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Design for the Environment/Alternatives To Traditional Book Publishing

Introduction
Today, books are an essential and crucial part of everyday life. The book is a symbol of knowledge and as an artifact represents investments – in the form of the author’s time, the publisher's capital and nature's trees used in paper and pulp mills. They provide us with a means of storing information that would otherwise be forgotten. For centuries, conventional books have been printed on paper derived from virgin materials. With the millions of books printed and in circulation today (3.10 billion unit sales in 2007 alone, ), the major concern that comes to mind is the impact of paper which is used for creating these books. About 17% of total world's wood consumption is caused due to paper production. This is a major environmental concern as trees are the major sources of CO2 sinks in the world. With the increasing awareness on global warming, newer cleaner alternatives to the traditional methods of publishing books are being considered.

The first alternative considers replacing printed books with e-Books in the effort to reduce the dependence on paper. The development of e-Books and e-Book Readers is still in its infancy. This is a niche product only accounting for 3% of the market share. These e-Book Readers such as Amazon’s Kindle and Sony’s Reader allow users to download and read books on a sharp resolution screen which closely resembles paper.

The second alternative considers publishing books using recycled paper...i forgot..oh yea and bio-degradable ink as opposed to using all virgin materials. Due to initiatives such as the Book Industry Treaties on Responsible Paper (Appendix 5) the number of books printed on recycled paper has increased to 6 million in 2000. Compared with producing a ton of paper from virgin wood pulp, the production of one ton of paper from discarded waste paper used half as the energy and half the water required for convention paper production. It results in 74% less air pollution and 35% less water pollution, saves 17 pulp trees, reduces solid waste going to landfills and creates 5 times the number of jobs. (Source: Earth Care, 1988).

All the analyses performed in this report are targeted towards a proposed client, who in this case is a typical university student in Canada. It is assumed that the student is enrolled in a 4 year engineering program (BASc) and is taking 5 courses per semester. It is also assumed that each course requires one course-related book and the student purchases all the books required for the duration of 4 years.

Project Information
Section 01, Group A15:

Jaiganesh Rajasekharan (DFE_Group_A15) Pradyumna Challa (Praschalla) Anand Krishnan (Anandk) Kabeer Girme (Kabeer.Girme)

EIOLCA
The EIO-LCA was performed on each of the three alternatives to analyse their individual environmental impacts. The environmental impact of the product was broken down into four categories: Air pollutants, Green House Gases, Energy Usage and Toxic releases. Each alternative is ranked from the best (3 points) to the worst (1 point) based on their environmental impacts in each of the aforementioned categories. The alternative with the highest points is the most environmentally friendly option based on EIOLCA. Fig. 3 shows the overall EIOLCA rankings of the three alternatives based on their environmental impact in each category. According to EIOLCA, Traditional Books are the most environmental friendly option as they are scored the highest, followed by e-Books and then finally Eco-Friendly Books.

SLCA
According to the SLCA ratings in Table 1, Eco-Friendly Books are the most environmentally friendly alternative while e-Books are the least environmentally friendly. Traditional books are ranked second, doing considerably better than e-Book Reader. Eco-Friendly Books are ranked the highest primarily because they printed on recycled paper using bio-degradable soy-based ink. On the other hand, traditional printed books have received a lower score because they use virgin materials and are printed using petroleum based ink instead. Books are ranked the lowest mainly due to the processes that take place during pre-manufacturing and manufacturing and lack of methods to dispose/recycle the product safely.

Table 1: Summary of SLCA Ratings for the 3 Alternatives

Cost Analysis
The life cycle costs are calculated for the purpose of weighing the potential environmental benefits associated with an alternative to its costs. Fig. 4 presents the total life cycle costs of the three alternatives being considered over the assumed lifespan of 4 years. According to the Fig. 4 in the long run, it is cheaper to buy and e-Reader than to buy printed books. Over the lifespan of 4 years, the e-Reader + e-Books end up cost only $1,108 whereas a student choosing Eco-Friendly Books options pays almost double the price ($2,135). Therefore based on a purely economic stand point, e-Book Readers are clearly the preferable choice, followed by traditional Books and finally Eco-Friendly Books.

Recommendation
We recommend using the traditional book publishing as the method of publishing books for the following reasons. Traditional books scored the best in EIOLCA, indicating that it is currently the most environmentally friendly option. Although Eco-friendly books are made from recycled paper and bio-degradable ink, the process used the make the recycled paper – pulp mills is a very polluting and energy intensive process – and therefore pollutes more than traditional books. In terms of life cycle costs, traditional books are a lot cheaper than Eco-Friendly Books but are still more expensive than e-Books. However, from the societal analysis, it was seen that most people would consider buying an e-Books only if they were 40+% cheaper than books. Given that the average cost of the traditional books are $1,712, e-Books would have to be priced at US $900 and lower for majority of the population to consider buying it. However, e-Books + e-Readers are currently priced at $1,108 thus making traditional books the preferable choice again.

Functional Unit
It has been assumed that the function of 40 books is fulfilled by 1 e-Book Reader. Therefore all the analyses in the article pertaining to the baseline and the first alternative is done for a 1,000,000 books and all the analyses for the second alternative for 25,000 e-book readers.

Traditional Books
The flow chart (Fig.5.) shows the life cycle of a book. These different processes are classified into five stages, namely Pre-production, Production, Delivery, Use and Disposal in the table below.

Table 2: Classification of all the processes involved in the life cycle of the book into five stages

To further define the scope we have considered the following:
 * Average cost of a new text book in the United States college book store is US$ 53 for the year 2006-2007.
 * Therefore the average cost of a book in 2008 dollars is US$ 56.60.
 * The publisher of these textbooks on an average incurs a cost that is 57.6% of the average price.
 * It has been assumed that 100% of the books produced from virgin materials are recycled.
 * It has also been assumed that the reader reads the book during the day and thereby utilizes sunlight as the only source of energy to read the book.

e-Book Reader
The flow chart (Fig.6.) shows the life cycle of an e-Book Reader.

E-Book Readers are being considered a viable alternative to paper. The main advantages of e-Book readers are their portability and the convenience of having multiple books on a single device. Furthermore, the user can instantly download e-books highlight paragraphs, cross check material from other books and read in the dark. The primary disadvantage of the e-Book Readers is the potential environmental costs in the production and disposal stage along with the high initial cost ($300).

Eco-Friendly Books
In the case of Eco-Friendly books, they are assumed to be made from 100% recycled paper. As opposed to the traditional system, the ink used is soy-based and is bio-degradable. Also, it is assumed that the paper used can only be recycled once and therefore 100% of books produced using this method end up in land fills at the end of their life. It has also been assumed that the reader reads the book in natural sunlight and thereby is not using significant electrical energy during its use stage.

Conventional Air Pollutants
Traditional Books

Power Generation and Truck Transportation sectors in that order contributes the most of the total NOx emissions released during the life cycle of a traditional book in addition to Power Generation topping and Truck Transportation sectors topping the SO2 and CO emissions categories respectively.

e-Book Reader

The major air pollutants are SO2, CO and NOx. Of these, the maximum SO2 was produced by the power generation and supply sector while the maximum CO and NOx were produced by the e-Book Reader manufacturing sector.

Eco-Friendly Books

The major air pollutant released by the industry is Carbon Monoxide and the largest contributor is Pulp Mills.

Greenhouse Gases
Traditional Books

Power Generation, Paper Mill and Truck Transportation sectors in that order contribute the most to the CO2 emissions during the life cycle of a traditional book. The release of other gases such as CH4, N20 and CFC are not significant enough when compared to the total CO2 emissions as observed in Fig.8.

e-Book Reader

CO2 is the most dominant green house gas. Power generation and supply leads to the largest release of CO2. The e-Book Reader manufacturing and battery manufacturing sectors contribute a small amount to the total impact, while the effect of the data processing and packaging sectors is almost negligible.

Eco-Friendly Books

It was found that all the sectors (especially Synthetic Dye and Pigment) have significant contributions to the GWP and CO2 emissions. This is because of the Petroleum based pigments that are used in this industry.

Energy Usage
Traditional Books

Power Generation and Paper Mill sectors in that order use most the energy consumed to publish the traditional books.

e-Book Reader

The power generation and supply needed for the use phase as well as the manufacturing phase in the life cycle of the e-book reader has the greatest energy consumption. The manufacturing stages themselves are also seen to contribute to the energy consumption while the data processing and packaging sectors are negligible.

Eco-Friendly Books

Natural Gas is used as an energy source to run the grinding, bleaching and de-inking machines in Pulp Mills and therefore count for the largest consumers of energy in the manufacture of recycled books.

Toxic Releases
Traditional Books

Heavy metals such as copper, zinc and nickel mining; paper mill and pulp mill sectors in that order contribute the most to the total air, land, air and underground releases during the life cycle of a traditional book. This demonstrates the disastrous effect the mining of heavy metals can have on the environment.

e-Book Reader

The toxic releases from the manufacturing and use stages are significantly higher than the rest. Battery manufacturing in particular has the greatest impact, while data processing has relatively almost no impact.

Eco-Friendly Books

Pulp Mills by far release the largest amount of toxic releases. This is expected, as this industry releases a lot of waste in the form of ink and other contaminants removed from paper, waste and unusable paper etc. The other major source of toxic releases is the similar Pulp and Paperboard Mills industry.

Traditional Books
Pre-Manufacturing and Manufacturing

Traditional books get a low score in the pre-manufacturing stage because they use paper produced from the virgin material wood, in addition to using petroleum based solvents, heavy metals and synthetic dyes in the printing ink manufacturing process. The processes by which ink and paper are made are also energy intensive and that is another reason for the low score in the pre-manufacturing stage. In the manufacturing stage, the traditional books get a medium range score. The main damper being that paper produced from virgin resources is being used as a raw material in the book publishing industry.

Distribution and Use

Published books need to be transported in trucks which release large amounts of gaseous residues, giving them a low score in the distribution stage. Use stage gets a 100% score given the assumption that the user reads the books in natural sunlight and does not consume any commercially produced energy.

Disposal

The disposal stage of the traditional books, as assumed is recycling. As recycling is an energy intensive process and releases a lot of liquid and gaseous residues, it gets a medium range score.

e-Book Reader
E-READER are very helpful in fact they give people that are not so smart a education

Pre-Manufacturing and Manufacturing

The materials which pose the greatest potential threat to the environment are the LCD screens and the circuit boards which contain minute amounts of virgin resources. Other components contain virgin metals such as steel, copper (mining), lithium (electrolysis), ABS (emulsion polymerization). In the production stage, lead, which is considered to be a poisonous material is used for the manufacturing of solder along with tin which is needed for the circuits. Glass along with silicon dioxide is used for the manufacturing of LCD screens. The production of all these materials along with the manufacturing of the e-Book Reader which is multi-stage complex process involving e-Reader assembly, printing of the circuit board  is energy intensive and leads to significant solid, liquid and gaseous residues. Due to this e-Book Readers receive a low score in the Pre-production and Production stages.

Delivery and Use

Shipping of the e-book reader is a one-time cost. Considering the long life span of the e-Book Reader, this is not the major cost of distribution. Use of the e-Book Reader focuses on charging the battery. The e-Book Reader has a charging time of 2 hours and has a life of approximately 15 hours, similar to a PDA. When compared with traditional paper, 11 hours of e-reader use along with server use and network use, equals the amount energy needed to print single paper copy. Due to the relatively low cost of delivery and use, the e-Book Reader gets high overall score in this category.

Disposal

The recycling of an e-Book Reader has been compared to that of a computer due to the similarity of components and the unavailability of data for the recycling for e-Book Readers in particular. The e-Book Reader contains PCBs, PCTs and other semiconductor related devices. Due to its complexity, the e-Book Reader has been given a low score in this category.

Eco-Friendly Books
Pre-Manufacturing and Manufacturing

No virgin materials are used in the manufacture of Eco-Friendly books. The paper is manufactured from used paper and the ink is vegetable based. The only energy used is in the transportation of paper to recycling centres and in Paper Mills to carry out the recycling process. Pulp and Paper Mills do not have any solid residues as its components are in a completely closed loop and all the inputs are re-used. However, they do have liquid residues (Manufacture of pigments and dyes) and gaseous residues (VOCs released during production). Overall, Eco-Friendly books receive a high score in the Pre-production and Production stages.

Delivery and Use

All packaging materials are made of recycled cardboard which is completely recyclable. Transportation using trucks is an energy intensive and also leads to liquid and gaseous residues. During its use, there is almost no usage of resources because, as stated earlier, the reader is assumed to be reading in broad daylight, thus ensuring that this sector is not energy or resource intensive.

Disposal

It is assumed that most of these books are recycled, however a good portion of them also end up in landfills. The other sectors (Energy Use, Solid, Liquid and Gaseous Residues) depend on the lifespan of a book which is typically very long and thus result in a score of four.

Cost Analysis
The direct costs for each of the three alternatives include the capital, operating and disposal costs.

Traditional Books
Fig.14. illustrates that a publisher spends about 32.2 cents per dollar per book for printing and editing. These costs also include other costs such as warehousing, storage, salaries etc [Refer: http://www.nacs.org/common/research/textbook$.pdf]. Therefore an engineering guess of the actual cost of ink and paper that is used in the book is about 8 cents per dollar per book. Fig.15. shows that the publishing cost of a book is about 57.6 cents per dollar per book. Cost of transportation is pegged at 1 cent per dollar per book. As recycling is quite similar to the pulping and paper manufacturing process[9] and as the cost of recycling also involves the cost of transportation from the consumer’s household to a recycling plant, the cost of recycling can be assumed as 9 cents per dollar per book. Therefore the total direct cost of the book is 75.6 cents per dollar per book, which equals to US$ 42.8.

Fig.16. below summarizes the direct costs involved in publishing of a traditional book. It also shows us what percent of direct costs are capital, operating and disposal costs.

e-Book Reader
As mentioned before, the e-Book Reader is a niche market and data about the capital costs is not available. For the purpose of this study, the capital costs of an e-Book Reader were compared with those of an “i-phone” in order to get meaningful estimates. The cost of production of one i-phone is US $265.3. The Sony Reader takes 2 hours to charge using an AC adapter of approximately 100 watts. The average cost for electricity in USA is 11c/kWh. Assuming 1 charge per day for a period of 4 years, the total number of hours of charging would be 2920. The energy consumed would be 292 kWh. Hence the total operating cost of an e-Book Reader would be US $32.12 for a period of 4 years. Servers needed for the storage of e-books consume 300W of power. Each server has a huge storage space (in terabytes) and contains a very large number of e-books, much greater than the 40 books required by the student. By performing same calculations as before, the total operating cost of one server is US $1156.32. This cost cannot be attributed to one e-Book Reader due to the capacity of a single server. It costs an average US $110 to recycle an old PC. Based on the size of the e-Book Reader, it is assumed that it takes 1 / 10 this cost which is US $11.

Eco-Friendly Books
Even though recycled books have the potential to cost more due to the production of vegetable and soy based inks, eco-friendly books have strived to stay in the same price range as traditional books by sticking to paperback editions where hardback editions could have been published. Since we assume that these books are made up of mostly recycled paper (more than 60%) which results in 100% of these books being disposed through landfills. The total disposal cost of one book is considered to be $0.039 (by considering a cost of $25.80 per Cubic yard * 0.0015 cubic yards)

Calculation of Capital Cost of an Eco-Friendly Book
Average Consumer Cost of a textbook: USD 120.00 (Total Direct Cost)

Net Unit sales of University Publishers in 2006: 31.4 million

Total Capital Costs = USD 6.630 Billion

Total Sales over time span of 4 years = 125.6 (31.4 million books/year * 4 years)

Capital Cost per Eco-Friendly book= USD 52.78

Societal Analysis
One of the major issues encountered in the debate of e-Books vs. printed books is the people preferences to reading text over a screen. The purpose of this analysis is to compare people's preferences of reading from a physical book to that of an e-book. A survey was conducted consisting of 17 engineering students at the University of Toronto. In general, majority of the people prefer reading from printed books over e-books. The results of the survey show that 29.4 % of the people would always buy books regardless of the cost of the e-Reader while only 11.8% of the people would always buy e-Reader regardless of its cost. The results also indicate that most people would consider buying the e-Reader only if it is priced at 41-60% the price of the printed book.


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Talk:Switching Power Supply Fundamentals/The Basic unregulated switching supply

seeTalk:EE Switching Power Supply Fundamentals


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Design for the Environment/Street Lighting in Residential Region

Introduction and Motivation
Street light illumination is critical to everyday life. Pedestrians and drivers at night receive not only convenience but also safety from the brightness. In residential areas, the most densely populated place at night, people will normally have higher expectation of illumination. Therefore, stable performance under frequent usage is the minimum requirement. The client of this project is builder-developers.For this project, low Pressure Sodium (LPS) lamp, is selected as our baseline. Although it is the most electrically efficient lighting product, the short lifetime is a crucial problem. Therefore new lighting technologies have to be introduced, and two of the most popular choices are Light-Emitting Diodes (LED) and induction lamps.

In our in-depth analysis, Life Cycle Assessment (LCA) on LPS, LED and Induction Lamp will be conducted using Economic Input-Output LCA (EIOLCA), Streamlined LCA (SLCA), and economic analysis. In addition to the LCA, we will also analyze their functional, societal and environmental aspects.

Scope and Assumptions in the Life Cycle Assessment
Analysis is taken place in the Great Toronto Area (GTA), operated under 110V and used as street lights in residential areas.

We assume the timeframe is 100,000 hours (the lifetime of one Induction Lamp) and illuminating area is 5,000 meters square (1 km in length and 5 m in width).And the number of lamps used for LPS, LED and Induction Lamps are 116,64 and 9.5 respectively.

In addition, every light bulb is in its ideal situation, which will not break until the end of its lifetime. In Section 4 [Economic Input-Output LCA (EIOLCA)], we need to use eiolca database (www.eiolca.net), therefore we need to multiply the numbers of lamps by one million, which are 116 millions of LPS, 64 millions of LED and 9.5 millions of Induction-lighting lamps. Furthermore, we also assume the products are all manufactured and transported by truck from the United State, and the packaging is the same for all three products.

The entire assuptions are summarized in the following table.

Project Information
MIE315 section 02, Team B21 April 7, 2009

 * Ka-Yeung Lee [Leekayeu]
 * Yatu Shi [Shiyatu]
 * Ping Kei Yan [Yanping]

Recommendation
After performing SLCA, EIOLCA and cost analysis for each of the light options, the modern Induction lamp is the way to promote green lighting. Reducing environmental impact and emissions are worthy goals which can make a difference in limiting environmental problem through reducing carbon dioxide emissions from electricity generation, decreasing waste and improving ease of recycling. Since street lighting consumes a significant amount of energy production, installing a lighting system that has greater energy savings is very essential.

Induction lamp is indeed the future of lighting. It is a way to implement environmentally friendly technology that reduces impact in areas such as conserving energy, reducing CO2 emissions, reducing materials consumption, reducing mercury consumption, as well as streamlining recycling issues.

Baseline: Low Pressure Sodium Lamp
The usual configuration of an LPS lamp is a discharge tube enclosed by a vacuum glass tube. The inner pipe contains solid sodium and a small amount of noble gases (normally neon and argon) to have the gas discharge started. The lamp initially produces red light to warm up the sodium in about 15 minutes. After that, orange / yellow light will be emitted. Human eyes are most sensitive to yellow light. It can be seen as an effective illumination light source. This property can reduce energy waste in emitting other colors of light, thereby increasing the electrical efficiency. In addition to output light, this unique feature also limits its application in other fields. At the same time, the short lifetime, (a maximum of 18,000 hours), is still a crucial problem for LPS future development.

Alternative 1: Light Emitting Diode
The high power LED Street lamp analyzed in this report is based on the model EvoLux 13 WATT LED BULB manufactured by The Earthtech Products. It is a 13 Watt bulb with clusters of LEDs in ABS housing.

Traditional LEDs are very tiny and produce a little amount of light, so we use high power LED lamps, which consist of cluster of LED array in a housing case, for street lighting. Those lamps require transformer to step down the electricity and heat sinks to remove the heat generated which is destructive to the LEDs.

The advantages of using LED lamps are their long life and high efficiency. For example, the EvoLux 13W model has a product life 50,000 hours, which is about 10 year of lighting (assuming it operates 12 hours a day). This can significantly reduce the environmental impact from transportation and solid waste produced from replacing the lamps.

Unlike traditional street lamps, which emit yellow colored light, LED lamps can generate pure white light. White light is more pleasing to human eyes “ and people can see and judge objects more accurately.

The downside of using LED for lighting is its higher cost per unit compared to other alternatives. For example, the price of the EvoLux is US$79.98. The high cost for LED lamps will discourage people from using them. Another disadvantage is that LED lamps require transformers to step down 110V electricity to its operating voltage (24V). There is power loss in the process and therefore the LED lamps may require more energy than its manufacturer’s claim.

Alternative 2: Induction Lamp
One of the modern solutions for lighting application is induction. Induction light is a system based on the compact fluorescent lamp. The composition of induction lamps is same as compact fluorescent lamps. In contrast with CFLs, where an electrode transfers power to the lamp, an induction lamp eliminates the electrode. Instead, there is an inductor inside the bulb connected to the ballast. The power is transmitted by means of electro-magnetic fields.

There are 3 major advantages of electrode less induction lamp:
 * 1) 	Less mercury per lamp than most commercial lamps;
 * 2) 	The solid amalgam mercury used is less volatile than the liquid mercury found in most lamps;
 * 3) 	Long 100,000 hour lamp life compared with other commercial lamps.

The life span is greatly extended as the electrode, the limiting factor of most lamps, is eliminated. The mercury found in every other light product is highly volatile liquid, while mercury in induction lamps is stable solid amalgam. During any onsite cleanup of broken lamps or disposal, a solid form is easier and safer to handle. Moreover, induction lamps uses less mercury compared to other commercial lamps

Economic Input-Output Life Cycle Analysis
From the SLCA in previous section and the graphs below, Induction Lighting has the least environmental impact during the pre-manufacturing and manufacturing stages. The manufacturing process emits the least air pollutants, greenhouse gases and toxic substances. It also uses the least amount of energy. The high level of environmental impact caused by LPS is due to its shot life span. In our timeframe, the fact that amount of LPS lamps needed is almost twice the amount of LED lamps and a magnitude of order higher than the amount of induction lamps needed results in vastly compounded energy consumption and environmental impact. On the other hand, LED lamp is slightly worse then Induction Lighting lamp and far better then LPS lamp in terms of energy usage.

Although LPS has the smallest air pollutants per unit lamp, the short lifespan results in more lamps are requried within the lifeframe (100,000 hours), which is about 12 times more than Induction lamp and 2 times more than LED.

From the graph above, induction lamps contribute least GWP (global warming potential) to the environment.

LPS is said to be the most elecrically efficient previously. But considering the entire life cycle of these three products, we find that much more energy is consumed by LPS, and it is mainly from the prodution of the product.

LED and Induction lamps both contain a small amount of mercury, but this toxic substance is not easily released, therefore it does not have a large effect to the environment. By analyzing the whole cycle, LPS has the largest reponsibility for this issue due to its large amount solid residues in the end of life.

From the results of EIOLCA, Induction Lighting lamp would be the best option available in street lighting, LED lamps closely follow behind and LPS lamps are the least attractive alternative.

Streamlined LCA
Assumptions:

 * 1) The delivery stages of all three alternatives are the same process. Only energy is used and gaseous residues are released.
 * 2) The lamps only consume electricity in the use stage. Thus only the energy use environmental stage is concerned.
 * 3) The lamps contain no liquid and therefore no liquid residues in disposal.

It is clear that the SLCA rating shows that Induction lamp is the most environmental friendly street lighting option. This is mainly because it exerts less environmental impact during the disposal stage, due to the long life span and the advanced design of the lamp. On average, induction lamp lasts 100,000 hours. Within the 5000m^2 area, 9.5 lamps are used which is much less than 63 lamps and 117 lamps usage for LED and LPS respectively further minimizing energy consumption, disposal emissions and harm to the environment. Moreover, the lamp is designed to increase the ease of disassembly and hence the ability of recycling. Another important issue brought by induction lamp will be the mercury inside the lamp. Since the mercury is in solid form rather than volatile liquid, the disposal of mercury becomes much simpler.

Although Induction lamp has the highest rating, it is obviously not perfect. If we look at the production phase, the scoring is low since there are large amounts of toxic materials such as lead used in the process of making the ballast, and intensive energy input during phosphor coating production. The problem is compensated by the long life span and the small number of lamp use.

All of the above is in comparison with LPS, with a short life span of 18,000 hours. Although the wattage is just 13 W, because of the fact that it uses 117 lamps within the time frame and control volume it to be the most energy inefficient alternative. Also the pre-manufacturing earns significantly lower scores because of the glass production and mining and extracting of virgin metals. Although Induction Lamp also experience the same problem in pre-manufacturing, but the impact is greatly lowered by the small amount of lamps. For same reason, the impact of LPS in disposal phase is significant due to the short life span.

Light emitting diode is the intermediate option between the two. The most significant impact is during the production stage where large amount of toxic materials are used in the process of manufacturing semiconductors. From the SLCA matrix, we can see that the score of each category fall between induction lamp and LPS since the life span and number of lamp usage falls between the two.

Comparison with result from EIOLCA
For the pre-production stage, the scores of the alternatives match with the result from EIOLCA. The same result which induction Lighting is better then LED while LED is better then LPS. However, when we focus on the production stage, LPS surprisingly scores higher then both LED and Induction Lighting. It is because materials used in LPS production is not toxic relative to those used in LED and Induction Lighting. Therefore it has the highest score for Material Choice. Production of LEDs releases liquid residues from semiconductor cleaning while manufacturing of LPS has little or negligible liquid residues. Thus it scores a higher mark. LPS is the worst in EIOLCA because of its highest demand in our timeframe. If we take that into account, the rating in SLCA may match the result from EIOLCA. However in the production stage of the SLCA, we cannot consider that effect together with all other factors easily. The overall rating matches the result from EIOLCA. Induction Lighting Lamps remain the best alternative while LPS is the worst.

Cost Analysis
The total cost is composed of direct operating cost, selling price, disposal cost and indirect cost. Direct operation cost is analysis for both summer and winter time. For indirect cost, it is assumed to be the cost of illness due to CO2 emission. The total cost for LPS, LED and Induction lamp are as follow. It turns put that induction lighting is the most economical.

The option with lowest cost is always the most desired one. The total direct cost incorporate the operation cost in both summer and winter and the unit cost. Indirect cost is mainly the cost of illness cause by air pollutant generated indirectly from street lighting.

From the results of the cost analysis, induction lamp has the lowest total cost, which is $11901.89 US, while operation cost is the highest. From our calculations, total operating cost for induction lamp is $1194.3; for LEDs and LPS the costs are $388.11 and $563.61 respectively because of the fact that each induction lamps consume 40W of power. But again, it is compensated by its long life span. The total cost of induction lamp relative to the 100000 hours time frame and 5000m^2 is much lower then the other two as only 9.5 lamps are needed. Induction lamps save cost in dealing with medication related to respiratory illness. The main reason of that is the significant small number of lamp used relative to the other two alternatives. Obviously, Induction lamp is a preferable option.

Street lighting is an essential need. Costing is also a very important issue for managing a city. For a long-term approach, Induction Lamps outperforms the other two lighting options in both direct cost and indirect cost. This alternative is most suited for future street lighting projects.

Low Pressure Sodium Lamp
LPS has had one hundred years development, and their functions are familiar to users. Changing the broken light bulbs is one of the most frequent maintenances in our normal life. Although this drawback is generally accepted, the large amount of residues creates immense trouble to society and the environment. This kind of glass product is everywhere in the landfills, because it is hard to natural decompose and expensive for recycling processes.

Induction Lamps
The major environmental concern of induction lamp is the mercury contained inside the lamp. But compared to other mercury containing commercial lamps, the mercury in induction lamp is in solid amalgam form rather than in form of volatile liquid.

The mercury amount is just 3.8 mg for a 40W lamp. Moreover the use of solid form mercury greatly reduces emission and improved the ease of recycling. As induction lamp significantly promotes energy saving with a longer lifespan and higher lumens then LPS lamps and LEDs, the mercury emission problem should be a negligible concern by society.


text:
User:JaredRodrigues

Always Wanted To Schedule

 * Topic

I've always wanted to learn how to snowboard and to start buying some of my gear for next season.
 * Research Component

History of snowboarding Types of gear The best mountains in the world
 * week 1

 * week 2

 * week 3

 * week 4

I'm going to call anyone I know that snowboards. See If they can take me up to the slopes before the season is truly over. Start researching on-line and at the library.
 * week 5

keep researching on-line and at the library. Finish my outline, and start working on my paper and presentation.
 * week 6

keep working on paper and presentation
 * week 7

Buy a piece of my gear.
 * week 8

I'm completely finished with my project.

title: User:JaredRodrigues


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text: Talk:ERP/Dual UOMs

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User:Azcolvin429

Find user page at: Andrew Z. Colvin

title: User:Azcolvin429


text: File:Cost of battery.jpg

title: File:Cost of battery.jpg


text: User talk:SKennedy

title: User talk:SKennedy


text:
User:Finnrind/monobook.js

mw.loader.load('https://meta.wikimedia.org/w/index.php?title=User:Finnrind/global.js&action=raw&ctype=text/javascript');

title: User:Finnrind/monobook.js


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User talk:LJasudavicius

Make a link from wikiversity to wikipedia
Use this : text to make a link from this project to wikipedia article.Crochet.david 08:07, 8 April 2009 (UTC)

Links
Dear LJasudavicius please consult the "making links" page, how to make internal and external links, and use the hint of Crochet.david abowe. I also want to ask you to avoid new page creation wit a sole Wikipedia link in a not-so-nice format. I will keep them now, but they might be deleted soon. Make any relevant changes asap, if you want them to stay. In case they will be deleted, and you want to add some more usefull content you can re-create them. But please avoid the abbreviations as the title. --Gbaor 16:30, 8 April 2009 (UTC)
 * Pages were deleted, as noted earlier. --Gbaor 07:38, 16 April 2009 (UTC)

welcome!
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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! --Gbaor 16:31, 8 April 2009 (UTC)

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Here you find many usefull stuff... --Gbaor 16:31, 8 April 2009 (UTC)

title: User talk:LJasudavicius


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User talk:Lucy1111

link to wikipedia
To make a link to wikipedia, use  detergent  instead of  detergent  .Crochet.david 11:28, 8 April 2009 (UTC)

title: User talk:Lucy1111


text:
User:Egm6322.s09/MIT's OpenCourseWare course(s)

MIT's OpenCourseWare

16.920J / 2.097J / 6.339J Numerical Methods for Partial Differential Equations (SMA 5212) Spring 2003 Lecture notes, Lecture 1: Notes. (classification of PDEs, etc.) Slides

2.062J / 1.138J / 18.376J Wave Propagation Fall 2006 Lecture notes Chap 1: Transverse Vibration of a Taut String, Longitudinal Vibration of an Elastic Rod, Traffic Flow on a Freeway, Wave Propagation in Arteries, Shallow Water Waves and Linearization, Sound in Fluids, Flexural Waves in a Beam on an Elastic Foundation.

2.035 Special Topics in Mathematics with Applications: Linear Algebra and the Calculus of Variations Spring 2007 Ref: Abeyaratne, Rohan. Lecture Notes on the Mechanics of Elastic Solids. Vol. 1, A Brief Review of Some Mathematical Preliminaries. Free e-book, 2006. Matrix algebra and tensor algebra, etc.. For eigenvalue problem of symmetric matrices, see Sec.3.3, p.45; right-hand and left-hand orthogonal matrices, p.46; coordinate transformation, Eq.(3.27), etc.

18.305 Advanced Analytic Methods in Science and Engineering Fall 2004 2nd-order PDEs, brief review, not detailed. 1st-order PDEs, method of characteristics. Separation of variables, for additional details, see our lecture notes.

18.306 Advanced Partial Differential Equations with Applications Spring 2004 Closest to what we are doing, with more advanced details.

18.06 Linear Algebra Spring 2005, video lectures by Prof. G. Strang. Good review of linear algebra. Lecture 21, eigenvalues and eigenvectors. Lecture 25, symmetric matrices. etc.


text:
User:Egm6322.s09.Three.ge/MyReport6

$$u(R,\theta,t)=0 \quad \theta \notin [\frac{-\pi}{4},\frac{\pi}{4}] \quad \forall \ t$$

Also,

$$u(r,\theta,t=0)=u_{0} \left [1-\left (\frac{r}{R} \right )^2 \right ]$$ Separation of variables applied to nonlinear PDE: Read the Handbook.

 HW: Solve the PDE:

$$f(x)(u_{x})^{2}+g(y)(u_{y})^{2}=a(x)+b(y)$$

Where:

$$\begin{matrix} f(x)=2x & g(y)=3y \\ a(x)=4x & b(y)=5y \end{matrix}$$

 HW: Summarize the handbook's general theory for separation of variables.

How to differentiate an integral.

$$\frac{d}{dx}\int_{\zeta=A(x)}^{\zeta=B(x)}F(x,\zeta)d\zeta=\int_{\zeta=A(x)}^{\zeta=B(x)}\frac{\partial }{\partial x}F(x,\zeta)d\zeta$$

Which becomes:

$$F \left[x,\zeta=B(x)\right]\frac {dB(x)}{dx}-F \left[x,\zeta=A(x)\right]\frac {dA(x)}{dx}$$

It should be noted that the principle of dimensional homogeneity must be satisfied for the previous equations.

$$\textrm{Let:} \ \textrm{  }\begin{matrix} \frac{d}{dx}\int_{\zeta=A(x)}^{\zeta=B(x)}F(x,\zeta)d\zeta=\alpha& &\int_{\zeta=A(x)}^{\zeta=B(x)}\frac{\partial }{\partial x}F(x,\zeta)d\zeta=\beta\\ F \left[x,\zeta=B(x)\right]\frac {dB(x)}{dx}=\gamma & &F \left[x,\zeta=A(x)\right]\frac {dA(x)}{dx}=\delta \end{matrix} $$

Thus,

$$[\alpha]=\textrm{the} \ \textrm{ dimension} \ \textrm{ of} \ \alpha=\frac{[F][G]}{[x]}=\beta=\gamma$$

Homogeneous and Non-homogeneous PDE's

For the general 2nd order PDE:

$$au_{xx}+2bu_{xy}+cu_{yy}+du_{x}+eu_{y}+fu+g=\mathcal D(u)$$

The differential equation is considered homogeneous if:

$$\mathcal D(u)=0$$

And non-homogeneous if:

$$\mathcal D(u)=f$$

Where f is a forcing function.

Classical Wave equation:

$$(c_{0}^{2})w_{xx}=w_{tt}$$

Exact solution, d'Alembert solution:

$$w(x,t)=\frac{1}{2} [f(x-c_{0}t)+ f(x+c_{0}t)]+\frac{1}{2c_{0}}\int_{x-c_{0}t}^{x+c_{0}t}g(\zeta)d\zeta$$

Separation of variables

The method of separation of variables seeks solve a PDE of order n by separating it into a series of n ODE's and then solving these ODE's. For a linear PDE this is done by assuming a solution that is a product of n expressions, with each expression being only a function of one independent variable.

For example, for a given PDE, the solution will be of the form:

$$u(x_{1},x_{2},x_{3},\cdots x_{n})$$

Where:

$$x_{1},x_{2},x_{3},\cdots x_{n}$$

are independent variables.

To use the method of separation of variables, one assumes that the solution may be written as a product of expressions, with each expression being a function of only one independent variable.

$$u(x_{1},x_{2},x_{3},\cdots x_{n})=X_{1}(x_{1})X_{2}(x_{2})X_{3}(x_{3}) \cdots X_{n}(x_{n})$$

Plugging this product of terms back into the PDE, one may separate the variables, and thus solve n ODE's to solve the PDE. (reference Zwillinger)

An example of Separation of Variables on a non-linear PDE is given below.

title: User:Egm6322.s09.Three.ge/MyReport6


text: File:Flashlight - Eiolca tables.pdf

title: File:Flashlight - Eiolca tables.pdf