Formal Report -e45

Team P-Squared Formal Report E-45: Personal Electric Generator May 1, 2009

Kevin Jordan

Garrett Brigman

Michael Denk

Sean Hennessy

Brian Dolder

Josh Matson

1. 

INTRODUCTION .............................................................................................................................................. 1 

2. 

PROJECT OBJECTIVE STATEMENT .......................................................................................................... 1 

3. 

PROBLEM DEFINITION ................................................................................................................................. 1  3.1.  3.2. 

PROJECT SCOPE............................................................................................................................................. 1  MAJOR RISKS ................................................................................................................................................ 2 

4. 

CUSTOMER NEEDS ......................................................................................................................................... 4 

5. 

PRODUCT SPECIFICATIONS ........................................................................................................................ 6  5.1.  5.2. 

6. 

MODIFIED LOW-COST SPECIFICATIONS ........................................................................................................ 6  MODIFIED HIGH-PERFORMANCE SPECIFICATIONS ........................................................................................ 7 

DESIGN PLAN FROM FALL SEMESTER .................................................................................................... 7  6.1.  6.2.  6.3. 

7. 

LOW-COST MODEL DESIGN PLAN ................................................................................................................ 8  HIGH-PERFORMANCE MODEL DESIGN PLAN ................................................................................................ 8  WEBSITE PLAN ............................................................................................................................................. 9 

PROTOTYPING EFFORTS ............................................................................................................................. 9  7.1.  7.2. 

8. 

LOW-COST MODEL PROTOTYPE ................................................................................................................... 9  HIGH-PERFORMANCE MODEL PROTOTYPE ................................................................................................. 12 

MANUFACTURING DOCUMENTATION .................................................................................................. 15  8.1.  8.2. 

9. 

LOW-COST MODEL MANUFACTURING DOCUMENTATION .......................................................................... 15  HIGH-PERFORMANCE MODEL MANUFACTURING DOCUMENTATION .......................................................... 26 

PROJECT WEBSITE ...................................................................................................................................... 28 

10. 

PROTOTYPE TESTING............................................................................................................................. 28 

10.1.  10.2.  10.3.  10.4.  10.5.  10.6.  10.7.  10.8.  10.9.  10.10.  10.11.  10.12. 

THEORY ...................................................................................................................................................... 29  EXPERIMENT 1 ............................................................................................................................................ 29  EXPERIMENT 2 ............................................................................................................................................ 30  EXPERIMENT 3 ............................................................................................................................................ 30  EXPERIMENT 4 ............................................................................................................................................ 31  EXPERIMENT 5 ............................................................................................................................................ 31  EXPERIMENT 6 ............................................................................................................................................ 32  EXPERIMENT 7 ............................................................................................................................................ 32  EXPERIMENT 8 ............................................................................................................................................ 33  EQUIPMENT USED ................................................................................................................................... 33  TEST PROCEDURE ................................................................................................................................... 35  EXPERIMENT REPEATABILITY................................................................................................................. 35 

11. 

TEST RESULTS ........................................................................................................................................... 37 

12. 

TECHNICAL JUSTIFICATION ................................................................................................................ 41 

12.1.  12.2. 

LOW-COST MODEL JUSTIFICATION ............................................................................................................. 41  HIGH-PERFORMANCE MODEL JUSTIFICATION ............................................................................................. 42 

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12.3.  12.4.  12.5.  13. 

REVIEW OF SPECIFICATIONS & NEEDS............................................................................................ 49 

13.1.  13.2.  13.3.  14. 

LOW-COST MODEL PERFORMANCE ............................................................................................................ 49  HIGH-PERFORMANCE MODEL ..................................................................................................................... 51  ORIGINAL PROBLEM ................................................................................................................................... 52 

COSTS & ECONOMIC ANALYSIS .......................................................................................................... 52 

14.1.  14.2.  14.3.  14.4.  15. 

WATER WHEEL CALCULATIONS ................................................................................................................. 42  GENERAL CONSIDERATIONS ....................................................................................................................... 47  ENERGY COST SAVINGS .............................................................................................................................. 48 

PROJECT COST ............................................................................................................................................ 52  PRODUCT COST ........................................................................................................................................... 52  LABOR REQUIREMENT SUMMARY............................................................................................................... 52  SALES FORECAST ........................................................................................................................................ 53 

STANDARDS, COMPLIANCE & CONCERNS ...................................................................................... 53 

15.1.  15.2.  15.3.  15.4.  15.5. 

SAFETY EVALUATION ................................................................................................................................. 53  ENVIRONMENTAL IMPACT STATEMENT ...................................................................................................... 54  APPLICABLE STANDARDS ........................................................................................................................... 54  REGULATORY COMPLIANCE ....................................................................................................................... 55  LEGAL ISSUES ............................................................................................................................................. 55 

16. 

CONCLUSIONS & RECOMMENDATIONS ........................................................................................... 55 

17. 

REFERENCES ............................................................................................................................................. 57 

18. 

APPENDIX A: EXPERIMENT DATA ...................................................................................................... 58 

18.1.  18.2.  18.3.  18.4.  18.5.  18.6.  18.7.  18.8.  18.9. 

EXPERIMENT 1 ............................................................................................................................................ 58  EXPERIMENT 2 ............................................................................................................................................ 59  EXPERIMENT 3 ............................................................................................................................................ 60  EXPERIMENT 4 ............................................................................................................................................ 61  EXPERIMENT 5 ............................................................................................................................................ 62  EXPERIMENT 6 ............................................................................................................................................ 63  EXPERIMENT 7 ............................................................................................................................................ 64  EXPERIMENT 8 ............................................................................................................................................ 65  REPEATABILITY DATA ................................................................................................................................ 66 

19. 

APPENDIX B: SAMPLE CALCULATIONS ............................................................................................ 67 

20. 

APPENDIX C: ADDITIONAL MACHINING & ASSEMBLY INSTRUCTIONS................................ 71 

21. 

APPENDIX D: MATLAB CODE FOR WATER WHEEL CALCULATIONS ..................................... 74 

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1. Introduction With the validation testing complete, the final step of the project is to fully document the project details, and submit key deliverables. This Formal Report contains all the information required to understand and reproduce the design team’s work over the last two semesters. The first few sections of the report are a review of the project definition. This contains a definition of the problem and scope, a list of identified customer needs, product specifications, and the design plan from the first semester. The next sections describe the prototyping process, with full manufacturing documentation and test results. These results are compared with the specifications in order to demonstrate that the original problem was solved. The document contains an economic analysis and some notes about standards and compliance, and ends with final conclusions and recommendations.

2. Project Objective Statement The team will develop a low-cost model and a high-performance model of a personal power supply for heating and lighting, using natural energy sources and salvaged auto parts for components by May 2009 with a budget of $900.

3. Problem Definition Billions of people in developing countries are without a reliable source of electricity. While there are many relief efforts going on in these countries, very few have the knowledge needed to construct alternative power supplies for the homes of these people.

3.1. Project Scope  In the Fall Semester, the design team decided to limit the scope of the project to include only the mechanical gearing and electrical conversion. The team assumes that the customer has access to a lowspeed, high-torque rotational input (such as a water wheel), and electrical load devices. The box diagram and project scope may be seen in Figure 1.

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Natural Power Source: Wind, water, etc.

Input Shaft Natural Power Source

Rotational Step Up:

Manipulator:

Gearbox, pulleys, etc.

Windmill, waterwheel, etc.

Output Shaft

Power Generation Unit: Alternator, Generator, etc.

Power Consumption: Low watt light and heat

Power Storage: Cell, Battery of Cells

 

Scope of this Project

 

 

 

 

 

 

 

 

Figure 1: Project box diagram with scope

3.2. Major Risks  The following risks were identified in the Fall Semester: •

Turning an alternator at high speeds may be difficult using natural energy sources.

o The natural energy sources the team is considering for this design will likely turn a shaft at a low speed (under 100 rpm). However, automobile alternators may be inefficient or inoperable at these speeds. o

•

Possible solutions: ƒ Use an automobile differential and/or appropriately sized pulleys and belts to increase the speed on the alternator shaft. ƒ Select an energy source that will turn a wheel at high speeds. ƒ Modify or select an alternator to operate at low speeds.

The intended user may not have the necessary tools or technical knowledge to construct and maintain the personal power supply. o An optimal design would likely require custom-machined parts to ensure reliability, efficiency, and sustainability. Producing these parts in an underdeveloped nation could

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o

•

be difficult. Also, a working personal power supply might require regular maintenance from an experienced technician. Possible solutions: ƒ Develop solution using few or no custom-machined parts. ƒ Manufacture generic parts domestically that will work for most designs. ƒ Train the user in maintenance procedures.

Creating a generic design plan to accept automobile parts from all car models will be difficult.

o Car manufacturers select and design alternators, differentials, and other parts to meet the specific demands of each car. As a result, a generic design would have to allow for varying power input/output, mounting hole configurations, shaft diameters, and other specifications. Verifying parts from every car model would be impossible. o

Possible solutions: ƒ Develop multiple prototypes; evaluate benefits and pitfalls of common components. Make recommendations for part selection. ƒ Create a specific plan using parts from a single, common car model.

•

Power losses on transmission lines may be too high for practical use. o Typical car alternators generate power at approximately 12V to match the voltage of the car battery. Because the voltage is low, current (I) must be high (50 Amperes or more) to transmit significant power. Transmission line losses (P) are calculated using the equation P=I2R, where R is the line resistance. Resistance increases with the length and gauge of the transmission line. o Possible solutions: ƒ Use low-gauge wires (large diameter) for transmission lines. ƒ Keep electrical loads near the energy source. ƒ Remove alternator rectifier components and use a transformer to obtain high voltage and low current. ƒ Carry batteries from generation site to place of need.

•

If alternator output voltage are low (12V), common light bulbs and heating coils that typically operate at 120V (or higher) will not work effectively. o Light and heat output of electrical loads (with resistance R) will be proportional to the power (P) dissipated. The power dissipated may be found using P=V2/R, where V is the operating voltage. By reducing the voltage from 120V to 12V, for example, a given load will dissipate only 1% of the power – and therefore give off only 1% of the light or heat it normally would. o Possible solutions: ƒ Use low-resistance electrical loads, like car headlights, that are meant for lowvoltage operation. ƒ Obtain higher voltage output (as described above) to use typical light bulbs and heating coils.

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4. Customer Needs In order to fully understand the needs of potential customers, the design team completed several interviews. The interviewees were individuals who are familiar with the abilities, needs, advantages, disadvantages, and customs of people in foreign countries. In order to obtain a comprehensive view of customer needs across the world, the team surveyed people with knowledge of several different areas of the world. The result of these surveys may be seen in Table 1 on the following page. From this list, the most important and relevant needs were formed into metrics. The team then developed product specifications in order to meet the customer needs as completely as possible.

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Question  Questions /Prompt No. 

Customer Statement 

Need No.

Hot weather, Hurricanes, Very Windy,  Weather Resistant (wind/water/cold) Very Rain,  Flooding, Snow 

3

Describe the weather 

10

How much money is available for  maintenance ?

2a

What language(s) are the citizens most  familiar with?

5

Customer Needs 

What's  most needed as far as  electricity? Refrigeration? Lights? Heat?

1

Reliable  Low Cost of Operation Pictorial of  Components Pictorial Wiring Diagram Instructions in Local Languages

2 3 4 5 6

Instructions in multiple languages

7

Lights

8

Heat

9

Heat for boiling water and showering 

Water Heater

10

Refrigeration to keep food longer 

Refrigeration

11

Television Cell Phone Charger Radio Cereal Grinder Water Pump Sound System Electrical Stoves

12 13 14 15 16 17 18

Hardly any, 50% of initial cost

English,Spanish,Mayan,  Xhosa,Portugese  Lights for studying at night and  general practicality  Heater for warmth,  for boiling water,  for cooking 

8

What types of devices do they wish to  power?  

Television for watching soccer  Charger for cell phones  Radio to follow politics  Power cereal grinder  Power for pumping well water  Power for church speakers  Cooking stoves 

9

How much money could be spent for a  personal generator?

People have minimal extra money,   People only earn $1‐2 a day

Low Cost 

19

12

What is the availability of machine  shops?

Shops are for industrial use only,  Shops are in town away from the  rural areas 

Minimal Tooling

20

13

Is cement readily available? 

Cement is readily available, Concrete  is cheap from local hardware store

Able to mount in Cement

21

Pamphlet/Manual

22

Local Car Parts/Automotive parts

23

Minimal Motorcycle Parts

24

Run on Water

25

Run on Wind

26

Run on Rain Power

27

14a 17 17a

18

20

15

Not available at all, Available only to  How available is computer and internet  students, Internet café in town but  access?  not in rural areas  Not very common, there are  Do most people have access to  junkyards/car salvage yards? junkyards in nearby towns  What are some common  car/motorcycle models sold in this  Motorcycles are not very common  country? Many Villages built on rivers, there is  lots of flowing water  There are open plains where its very  Are there accessible rivers/streams or  windy.  large areas of open plains?  During rainy season and down‐pours  all the villages have roofs which could  be used to generate power Do you have any other ideas or  thoughts? What is the technical aptitude of the  people? 

It has to be easily incorporated into  Practical (Quiet/Small/Out of the Way) their lifestyle Citizens would like to be involved in  Citizen Involved Building  construction None to very little 

Require Simple Tools 

28 29 30

Table 1: Customer needs identified from surveys

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5. Product Specifications During the designing and building process of the personal power supply, the original product specifications (Table 2) for our project changed to ensure that the power supply would be functional. Originally, we created only one set of specifications, but to match our design plan, we divided it into two sets of specifications, one for each configuration. Metric No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Need Nos. 1,4 6,7 29 8‐18 8‐18 8‐18 19 2,3 20,30 21 4,5,22 23 24 25‐27 25‐27 28

Specifications Specifications Protect it from elements Multiple translations of instructions Able to be built on site Power Output Electrical Output Output Frequency Cost of Parts Cost of Operation Parts needing Tooling Cement Foundation Used Pictorial Instruction Pamphlet Distance to Car parts Number of Motorcycle Parts needed Torque input required Speed input required Obstructs daily life

Imp. 1 2 1 3 3 4 2 3 2 3 2 4 5 1 1 4

Nominal Yes 3 Yes 0.5 12 15 250 5 3 Yes Yes 50 3 4.77 1000 Yes

Ideal Yes 7 Yes 1.9 14 0 100 0 0 Yes Yes 10 0 6.05 3000 Yes

Units Binary Integer Binary kW Volts DC Hertz USD USD per Month integer binary binary km Integer N‐m rpm binary

Table 2: Original specifications

5.1. Modified Low­Cost Specifications  Some of the original specifications have been removed entirely from both revised sets, for various reasons. For instance, we removed “Multiple translations of instructions” because we will be unable to provide these translations. However, since many translation websites currently exist on the Internet, our instructions must merely appear online in English. Since the goal is to charge a 12V battery, “Output Frequency” makes little sense. The output will be DC electrical power. Also, the “Distance to Car parts” is not something we can either specify or test. It is merely a qualification for any potential customers. Finally, in order to clarify, “Able to be built on site” has been changed to “Able to be assembled on site”. The low-cost prototype is designed specifically for people in developing countries. From discussions with our project advisor, we have decided to make some specification changes. Since the output only needs to be enough to charge a battery, some requirements have been relaxed. These revised specifications may be seen in Table 3.

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Table 3: Revised specifications for Low-Cost model

5.2. Modified High­Performance Specifications  The high-performance prototype has similar changes to the specifications. However, higher expectations may be set for this prototype. The nominal and ideal speed inputs were changed to 500 rpm and 1000 rpm respectively. The reason for this was because the Wind Blue alternator does not require as high of an input speed as the car alternator to generate power. The expected power output is greater than the low-cost model as well. The revised specifications may be seen in Table 4.

Table 4: Revised specifications for High-Performance model

6. Design Plan from Fall Semester The design team generated several concepts for consideration during the Fall Semester. These concepts were all rated for cost, performance, and required labor. From these concepts, two final concepts emerged.

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6.1. Low­Cost Model Design Plan  The Low-Cost model of the Personal Power Supply was designed to have components that could all be salvaged from used cars or other machines. The concept image may be seen in Figure 2.

  Car alternator  10:1 gearing through  transmission and pulleys 

Car battery 

Waterwheel  input shaft 

Wood mounting  Bracket anchored  in cement base 

Figure 2: Low-Cost model mockup

6.2. High­Performance Model Design Plan  The idea for the High-Performance model was to loosen the restrictions of the Low-Cost model, allowing the team to use more ideal components in the system – rather than salvaged components. In this model, a permanent magnet alternator is used instead of a car alternator. The PM alternator generates more power at lower speeds. This allows a simpler (and therefore more reliable) gearing system. The concept image may be seen in Figure 3.

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Figure 3: High-Performance mockup

6.3. Website Plan  Rather than forming a plan to sell the products to consumers, the team decided to share the group efforts with the world. The group decided that the best way to share this information was through a website that would follow our project. At the end, the team hoped to have all of the project deliverables available for viewing.

7. Prototyping Efforts From the beginning of the Spring Semester, the design team had the goal of constructing two versions of the Personal Power Supply. Since the team was only able to acquire one water wheel simulator, it was important to make the prototypes easily configurable. The result of the team’s efforts may be seen in this section.

7.1. Low­Cost Model Prototype  The Low-Cost design (see Figure 4) utilized two stages of gearing, totaling a gear ratio of 97:1. This was a necessary component of this design because we used a lower cost, higher amperage alternator. The alternator needed around 1200 rpm to begin outputting current. This is much higher speed than the High Performance design and therefore required much more gearing to make a realistic speed at the water wheel. With this gearing we were able to charge a battery at about 13 rpm input at the water wheel. This is not only a very achievable speed, but one that was easily tested with our equipment.

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Figure 4: Low-Cost block diagram

One limiting factor in our equipment was the torque. Along with speed increasing throughout our system, torque decreased. Because of this the low cost design requires a much higher torque requirement at the water wheel than the High Performance design. The motor in our testing, simulating a water wheel, was the limiting factor and only allowed us an input speed of just under 16 rpm before it maxed out on torque. At this point we were able to achieve 350 Watts output at 13.5V. A photo of the Low-Cost prototype may be seen in Figure 5.

Figure 5: Prototype of Low-Cost model

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The Bill of Materials for the Low-Cost model may be seen in Table 5. This table includes the required quantities of each part, along with cost information for each part. The ‘Salvaged Cost’ is an estimate of the cost of each part if found in working condition in a salvage yard in the United States. Note that it would be impossible to predict the costs of parts found in every country of the world. However, every part in the LowCost model could either be salvaged or replaced with an equivalent part found in a salvage yard. Item No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Description Waterwheel Sprocket, 9 Teeth, for #60 Chain, 3/4" Pitch, 1" Bore, Hardened Steel Teeth Sprocket, 60 Teeth, for #60 Chain, 3/4" Pitch, 1" Bore, Hardened Steel Teeth Intermediate Shaft, 1" Diameter, 13" Long Flywheel, Dodge Dakota, and Hub Pinion Gear, Dodge Dakota Alternator Intermediate Shaft/Coupling Pillow Block Bearing, 1", Self-aligning Delco-Remy Alternator, Chevy Suburban Mounting Plate, A36 1/2” Plate Steel Supporting Columns, ASTM A36 2” Square Tube Stock Base, ASTM A36 12”x3” Channel Iron

Angle Iron, ASTM A36 2”x2”x1/4” Alternator Bracket, Delco‐Remy, ASTM A36 1/2" Plate Steel # 60 Chain, 3/4" Pitch, 5 ft Car Battery, 12 Volt

Quantity 1 1 1 1 1 1 1 3 1 1 1 1 2 1 1 1 Total Cost

Table 5: Bill of Materials for the Low-Cost model

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Our Cost N/A 21.01 27.62 3.85 54.95 10.27 2.50 25.44 42.24 18.60 10.60 20.59 10.12 15.00 41.15 143.00 $446.94

Salvaged Cost N/A 7.00 9.21 2.96 27.48 3.42 1.92 25.44 42.24 14.31 8.15 15.84 7.78 11.54 20.58 35.75 $233.62

7.2. High­Performance Model Prototype  Our High Performance design (see Figure 6) utilized only one stage of gearing, along with a permanent magnet alternator to create a higher performing generator at lower input torque requirements. Along with this lower torque requirement came a higher cost for the permanent magnet alternator. We also implemented a charge controller with our design. This allowed us to setup a more permanent charging solution which could be implemented as part of either a grid-tied or off-grid system. The charge controller is able to be set through a computer interface to charge and discharge at different voltage ratings. This will prevent over-charging of the battery bank and allow charging of different voltages of banks.

Figure 6: High-Performance block diagram

The gearing in this design is simple as a more complicated design is unnecessary for this low of speed requirements in the alternator. The gearing consists of a simple 14.5:1 gear ratio achieved with a flywheel and pinion from a starter out of a 1999 Dodge Dakota engine. A photo of the High-Performance prototype may be seen in Figure 7.

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Figure 7: Prototype of High-Performance model

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The Bill of Materials for the High-Performance model may be seen in Table 6. This table includes the required quantities of each part, along with cost information for each part. The ‘Salvaged Cost’ is an estimate of the cost of each part if found in working condition in a salvage yard in the United States. Some items, including the Charge Controller and WindBlue Alternator, may not be available in any salvage yard. The costs of these parts are simply copied into ‘Salvaged Cost’, even though the parts would need to be purchased new. Item No. 1 2 3 4 5 6 7 8 9 10 11

Description Waterwheel Flywheel, Dodge Dakota Pinion Gear, Dodge Dakota Alternator Intermediate Shaft/Coupling Pillow Block Bearing, 1", Self-aligning Wind Blue Permenant Magnet Alternator

Angle Iron, ASTM A36 2”x2”x1/4” Alternator Bracket, Wind Blue, ASTM A36 1/2" Plate Steel Base, ASTM A36 12”x3” Channel Iron Car Battery, 12 Volt Charge Controller

Quantity 1 1 1 1 1 1 2 1

Cost N/A 54.95 10.27 2.50 8.48 249.00 10.12 15.00

Salvaged Cost N/A 27.48 3.42 1.92 8.48 249.00 7.78 11.54

1

20.59

15.84

1 1 Total Cost

143.00 140.54 $654.45

35.75 140.54 $501.75

Table 6: Bill of Materials for High-Performance model

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8. Manufacturing Documentation This section contains the required documentation for manufacturing each model of the Personal Power Supply. Each component has a thorough description of the part, including materials, required tools, construction time, and an image of the part. Assembly drawings show how each component fits into the final product. See Appendix C: Additional Machining & Assembly Instructions for special notes on creating the more complicated components.

8.1. Low­Cost Model Manufacturing Documentation  The following gives a description of each major component needed to be manufactured for the low cost model. A detail drawing for each piece is also provided. At the end of the section, an overall assembly drawing is shown which includes items that were both manufactured and purchased by the team. 1.) Alternator Mounting Bracket and Base: The alternator mounting bracket and base is designed to hold either the Delco-Remy or Wind Blue alternator. It contains the following items from the BOM: 12, 13 and 14 A. BOM Item 13 - 2”x2”x1/4” Angle Iron (x2) ™ Tools Required: Vertical axis mill and small hand drill ™ Material: AISI/SAE 1018 hot roll steel 2”x2”x1/4” Angle Iron ™ Estimated Construction Time: 30 minutes each ™ Detail Drawing: Figure 8

Figure 8: Angle Iron

B. BOM Item 14 – Delco-Remy Car Alternator Bracket ™ Tools Required: Vertical axis mill and small hand drill Formal Report Project: E45 – Personal Power Supply

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™ Material: AISI/SAE 1045 hot roll 1/2" plate steel ™ Estimated Construction Time: 30 minutes ™ Detail Drawing: Figure 9

Figure 9: Alternator Bracket

C. BOM Item 12 – Base ™ Tools Required: Vertical axis mill ™ Material: AISI/SAE 1045 13”x3” channel iron ™ Estimated Construction Time: 45 minutes ™ Detail Drawing: Figure 10

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Figure 10: Base

D. Alternator Mounting Bracket and Base Assembly ™ Tools Required: MIG Welder and Wrench ™ Estimated Assembly Time: 20 minutes ™ Total Construction Time: 2.6 hours ™ Assembly Model: Figure 11 (Alternator and pinion gear also shown)

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7/16” Bolt,  Nut, and  Washer 

Fillet Weld

7/16” Bolt,  Nut, and  Washer 

Figure 11: Alternator mounting bracket and brace

2.) Intermediate Shaft and Mount: This is a mounting scheme that allows for an additional gearing stage through an intermediate shaft. The intermediate shaft will transmit power delivered from the chain and sprocket to the pinion and flywheel system. The intermediate shaft is supported by two 1” pillow block bearings (BOM item 15) which are fastened to this mount. This mount contains the following items from the BOM: 4, 8, 10, 11, and 12. A. BOM Item 4 – Intermediate Shaft ™ Tools Required: Lathe ™ Material: AISI/SAE 1045 hot roll steel 1” bar stock ™ Estimated Construction Time: 20 minutes ™ Detail Drawing: Figure 12

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Figure 12: Intermediate shaft

B. BOM Item 10 – Mounting Plate ™ Tools Required: Hand drill ™ Material: AISI/SAE 1045 hot rolled 1/2” plate steel ™ Estimated Construction Time: 20 minutes ™ Detail Drawing: Figure 13

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Figure 13: Mounting plate

C. BOM Item 11 – Supporting Columns (x2) ™ Tools Required: Steel saw ™ Material: AISI/SAE 1045 hot rolled steel 2” square tube stock ™ Estimated Construction Time: 10 minutes each ™ Detail Drawing: Figure 14

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Figure 14: Supporting columns

D. BOM Item 12 – Base – see section 1 E. BOM Item 8 – 1” Self Aligning Pillow Block Bearing (x2) ™ Tools Required: Allen wrench ™ Material: Purchase ™ Estimated Construction Time: Purchase ™ Detail Drawing: Figure 15

Figure 15: Pillow block bearing

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F. BOM Item 5 – Fly wheel and Hub ™ Tools Required: Lathe, mill, steel saw, hand drill, and wrench ™ Material: AISI/SAE 1045 hot rolled steel ™ Estimated Construction Time: 2 hours ™ *See Appendix C: Additional Machining & Assembly Instructions for detailed instruction regarding this piece* ™ Detail Drawing: Figure 16

Figure 16: Hub

G. Intermediate Shaft and Mount Assembly ™ Tools Required: MIG welder and wrench ™ Estimated Assembly Time: 45 minutes ™ Total Construction time: 2.33 hours ™ Assembly Model: Figure 17 (Fly wheel and small sprocket are also shown)

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  7/16” Bolts,  Nuts, and  Washers 

Fillet Weld

Figure 17: Intermediate shaft and mount assembly

3.) Alternator Connecting Shaft/Coupling: This piece allows for the connection between the car pinion gear and the Delco-Remy alternator. This could have been a purchased component, but the team elected to manufacture it ourselves. A. BOM Item 7 – Alternator Connecting Shaft/Coupling ™ Tools Required: Lathe, hand drill, and Allen wrench ™ Material: AISI/SAE 1045 hot rolled steel 1” bar stock ™ Estimated Construction Time: 1 hour ™ Detail Drawing: Figure 18

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Figure 18: Alternator coupling

4.) Purchased and Assembled Components: The following details the tools required and assembly times for the low cost model’s purchased components. A. Chain and Sprockets Assembly (BOM Items 2, 3, and 15) ™ Tools Required: Chain tensioner, Allen wrench, and screw driver ™ Estimated Assembly Time: 50 minutes B. Flywheel, Pinion, and Alternator Assembly (BOM Items 5, 6, 7, 8, and 9) ™ Tools Required: MIG welder, wrench, and Allen wrench ™ Estimated Assembly Time: 2 hours

5.) Overall System Assembly: Figure 19 shows an exploded assembly drawing for the low cost model. The overall manufacturing and assembly time follows.

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  1 

4 3 

5

7 

14 9

15

2  6 8  10

13

11 

12

Figure 19: System assembly of the Low-Cost model

Overall Manufacturing and Assembly Time: 10.75 hours 6.) Electrical Wiring: See Figure 20 for wiring diagram. All connections must be secure, and wires must be insulated from other wires. Where marked, wires must be 12 AWG or larger. Other wires must be 22 AWG or larger.

Figure 20: Wiring Diagram for the Low-Cost model

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8.2. High­Performance Model Manufacturing Documentation  The following gives a description of each major component needed to be manufactured for the high performance model. The specific manufacturing details are identical to those presented in the low cost model section, so they are not shown again here. At the end of the section, an overall assembly drawing is shown which includes items that were both manufactured and purchased by the team. 1.) Alternator Mounting Bracket and Base: The alternator mounting bracket and base is designed to hold either the Delco-Remy or WindBlue alternator. It contains the following items from the BOM: 7, 8 and 9. 2.) Alternator Connecting Shaft/Coupling: This piece allows for the connection between the car pinion gear and the WindBlue alternator. This could have been a purchased component, but the team elected to manufacture it ourselves. It is BOM item 4. 3.) Purchased and Assembled Components: The following details the tools required and assembly times for the low cost model’s purchased components. A. Charge Controller Wiring Connections (BOM Item 10 and 11) ™ Tools Required: Screwdriver and wire cutters ™ Estimated Assembly Time: 1.5 hours C. Flywheel, Pinion, and Alternator Assembly (BOM Items 2, 3, 4, and 6) ™ Tools Required: MIG welder, wrench, and Allen wrench ™ Estimated Assembly Time: 2 hours ™ *See Appendix C: Additional Machining & Assembly Instructions for detailed instruction regarding the flywheel coupling and hub* 4.) Overall System Assembly: Figure 21 shows an exploded assembly drawing for the high performance model. The overall manufacturing and assembly time follows.

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7 

8 

9 

Figure 21: System assembly of the High-Performance model

Overall Manufacturing and Assembly Time: 9.1 hours 5.) Electrical Wiring: See Figure 22 for wiring diagram. All connections must be secure, and wires must be insulated from other wires. Where marked, wires must be 12 AWG or larger. Other wires must be 22 AWG or larger.

Figure 22: Wiring Diagram for the High-Performance model

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9. Project Website The team created a website (www.muelectric.org) using the Google Blogger interface. We chose this method of information sharing for two reasons. First, this interface is very intuitive to implement and would allow all members of the community, even those who are less “web savvy”, to post and comment on our project. Second, Google will continue hosting our website even after we have completed our term at Marquette. This will allow future generations to view our work. A screen shot of the website may be seen in Figure 23.

Figure 23: Screen shot of the project website

The project website contains photos, videos, instructions, and other relevant information needed for constructing a Personal Power Supply. For international users, Internet translators will allow individuals to view the information in their native language.

10. Prototype Testing The purpose of these experiments was to test each prototype and compare the results to the product specifications. In particular, the power outputs, electrical outputs and speed inputs were the main Formal Report Page 28 of 79 Project: E45 – Personal Power Supply Revision 1.0

focus of the experiments. With the results, adjustments have been made to the prototypes to meet the product specifications.

10.1. Theory  The best way to obtain the most information about a rotating power system would be to test the system at various speeds and varying the electrical load. This should give the team enough information to verify our specifications, or make recommendations for changes. Our simulated water wheel (the gear motor) has a frequency input that generally corresponds to input speed. This correspondence will remain true, unless the motor is being overloaded. Since the motor controller varies the voltage linearly with the frequency, the system inputs are motor frequency, motor voltage, and DC electrical load. The electrical loads used in the experiments are an open circuit (no load) and an automotive battery. Charging the battery will result in a drop in rotational speeds, and a drop in the DC output voltage. The output current will be non-zero, and power will transfer to the battery. The speed will decrease simply because the electrical load on the alternator creates a mechanical load on the gearing. This increased mechanical load will be in the form of increased torque, which will slow the generator. Increasing the motor frequency and motor voltage should increase the torque and speed of the entire system. Since the torque and speed increases, the power transfer to the load should increase as well. With a battery as a load, this could simply result in higher current. With no load, this will result in a higher voltage, and greater thermal losses. In the event of an overloaded gear motor, increasing the frequency would increase the torque and speed only slightly, while greatly decreasing the motor efficiency. For this reason, the team took caution not to make sharp increases in input frequency.

10.2. Experiment 1  The first experiment (Figure 24) was created using two sets of gearing and a WindBlue alternator. The first set of gearing consisted of a set of sprockets and chains with a 6.67:1 ratio. The second set of gearing included a flywheel and pinion with a 14.5:1 gear ratio. This experiment was conducted without an electrical load.

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Figure 24: Configuration for Experiment 1

10.3. Experiment 2  The second experiment (Figure 25) was conducted with the same setup as the first experiment except that a charge controller and 12V battery were used as an electrical load.

Figure 25: Configuration for Experiment 2

10.4. Experiment 3  The third experiment (Figure 26) was performed using a single set of gearing and a Wind Blue alternator. The set of gearing consisted of a flywheel and pinion with a 14.5:1 gear ratio. This experiment was conducted without an electrical load.

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Figure 26: Configuration for Experiment 3

10.5. Experiment 4  The fourth experiment (Figure 27) was conducted with the same setup as the third experiment except that a charge controller and 12V battery were used as an electrical load. This is the preferred configuration for our High-Performance model.

Figure 27: Configuration for Experiment 4

10.6. Experiment 5  The fifth experiment (Figure 28) was performed using both stages of gearing and the Delco-Remy car alternator. The first set of gearing consisted of a set of sprockets and chains with a 6.67:1 ratio. The Formal Report Project: E45 – Personal Power Supply

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second set of gearing included a flywheel and pinion with a 14.5:1 gear ratio. This experiment was conducted without an electrical load.

Figure 28: Configuration for Experiment 5

10.7. Experiment 6  The sixth experiment (Figure 29) was conducted with the same setup as the fifth experiment except that a 12V battery was used as an electrical load. This is the preferred configuration of our LowCost model. Despite having a greater number of parts, each component in this setup could feasibly be salvaged in a developing country.

Figure 29: Configuration for Experiment 6

10.8. Experiment 7  The seventh experiment used the same configuration as Experiment 5, except with a larger gear motor. The new water wheel simulator includes a motor controller and a 2.0hp, 1750 rpm motor with a 40:1 gear reducer. Formal Report Project: E45 – Personal Power Supply

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10.9. Experiment 8  The eighth experiment used the same configuration as Experiment 6, except with a larger gear motor. The new water wheel simulator includes a motor controller and a 2.0hp, 1750 rpm motor with a 40:1 gear reducer. With the increased power of the new motor, the team was able to more fully test the capabilities of the Low-Cost model.

10.10.

Equipment Used 

To record data in our experiments, we used a variety of measurement equipment. The input variables, including motor frequency, line-to-line voltage, and line current were recorded from the display on the Magnetek GPD 515 motor controller we used to drive the motor. This controller, seen in Figure 30, has sensors that measure these values accurately.

Figure 30: Motor controller (left) and kill switch (right)

In order to simulate a water wheel, we used a Nord Flexbloc gear reducer for Experiments 1 through 6, shown in Figure 31. This reducer is driven by a 1.0hp motor, with an output speed between zero and 58 rpm. This low-speed, high-torque input is similar to what one may expect from an actual water wheel. Experiments 7 and 8 used a 2.0hp Flexbloc reducer to further test the system capabilities.

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Figure 31: Gear motor used as a simulated water wheel

For speed measurements, the team used an optical tachometer. We placed reflective tape on the flywheel, 60-tooth sprocket, and the alternator shaft for the tachometer to read. Every time the tachometer ‘sees’ the reflective tape, it calculates the time between revolutions, and displays the speed in revolutions per minute (rpm). Electrical measurements, including voltage and current, were measured primarily with Fluke multimeters (see Figure 32). Current measurements were taken by wiring the meters in series, while voltages were measured in parallel. All of the alternator voltage and current measurements were measured in this fashion. For Experiment 4, battery voltage and current measurements were taken from the charge controller sensors. These values were sent via serial connection to a laptop, where the data was read.

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Figure 32: Multimeters used for voltage and current measurements

10.11.

Test Procedure  

Each test point for the six experiments was conducted in a similar fashion. An input motor frequency was entered into the motor controller. The motor frequency typically relates to both the motor voltage and operating speed. After transient conditions fade away, the motor voltage and current measurements were taken. Speed measurements were also taken on each rotating shaft. Finally, output voltage and current measurements were taken. In Experiments 2, 4, and 6, we found that the input motor struggled to maintain a safe operating speed. As the motor became overloaded, it failed to increase speed, and the system began to vibrate. For this reason, some of the data points were impossible to take. This was no longer a problem for Experiments 7 and 8, which used the larger gear motor.

10.12.

Experiment Repeatability  

The intent of this section is to provide the reader with a measure of the repeatability of the measurements performed in this experiment. To do this, a motor operating speed was chosen (19 Hz) and measurements of motor current, motor voltage, input speed, output current, and output voltage were taken. The system was then restarted and the measurements repeated. The results in generator power output and efficiency are shown below in Figure 33 and Figure 34. The spread in the calculated values is shown in each figure.

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Figure 33: Repeatability of Generator Power

Figure 34: Repeatability of Generator Efficiency

The spread in the calculated values is clearly minimal (Power: 1.6%, Efficiency 1.9%). The largest concern is the variability in input speed (0.65 rpm or 4.9%), although even this amount of variability still provides the team with adequate confidence that the measurements taken are reliable. From this point on, it will be assumed that one measurement point is sufficient to characterize the system’s performance (i.e. only one measurement is taken at each operating speed). Formal Report Project: E45 – Personal Power Supply

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11. Test Results The following plots were obtained directly through the measurement procedure outlined in the previous section for the experiments. The relevant data shown here includes the following: open circuit voltage, generator power output, and generator efficiency. In each case, the relevant parameter is shown as a function of the input speed. Additionally, a comment regarding the uncertainty of each measured and calculated value is necessary. The uncertainty of all calculated values was determined using what is termed the root-sumsquares method (RSS – See Reference 9). Furthermore, in each of the proceeding plots error bars are included. However, in almost every case the magnitude of the uncertainty is on the order of the data point size, so it is not visible. To still provide the reader with an estimate of the uncertainty, the maximum uncertainty is shown in each figure caption. Refer to the Appendix B for an example calculation of each uncertainty. The open circuit voltage was measured for three cases: WindBlue at 100:1 gear ratio, WindBlue at 14.5:1 gear ratio, and Delco-Remy at 100:1 gear ratio. These values are the result of experiments 1, 3, and 5, respectively, and are shown in Figure 35 and Figure 36. They are on two separate plots due to scaling issues. 80.00 70.00 100:1 - No Load

60.00 Wind Blue Voltage (V)

14.5:1 - No Load

50.00 40.00 30.00 20.00 10.00 0.00 0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

Input Speed (rpm)

Figure 35: Open Circuit Voltage for WindBlue Alternator using 100:1 and 14.5:1 Gear Ratios (Experiments 1 & 3) – Maximum Uncertainty: ±0.01 V, ±0.012 rpm

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0.350

0.300

Voltage (Volts)

0.250

0.200

0.150

0.100

0.050

0.000 0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

Input Speed (rpm) Figure 36: Open Circuit Voltage for Delco-Remy Alternator Using 100:1 Gear Ratio (Experiment 5) – Maximum Uncertainty: ±0.002 V, ±0.007 rpm

Figure 35 and Figure 36 show linear relationships between alternator voltage and input speed under no applied electrical load. While these trends will be altered when a load is applied, the output should still maintain a linear form. It should be noted that the entire voltage versus speed curve over the alternator’s entire operating range is not linear. However, in the region in which it is being operated, the alternator does display highly linear behavior. It is not until much higher voltages that significant deviation from this trend is observed. Note that the Delco-Remy alternator must be energized (where by energized we mean provided with field current) by a battery before it can generate a significant voltage. This is why the open circuit voltages in Figure 36 are very low.

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The results from Experiment 2 are more bountiful (again, the reason for this will be discussed in the analysis), and are shown in Figure 37. Using the 14.5:1 gearing ratio, an appropriate charging voltage for the battery was achieved at approximately 40 rpm. From that speed on, a significant increase in output power was observed as the speed increased. The difference between the square data points and the triangular data points, for a given speed, is an estimate of the power lost within the generation system. 700 Motor  Power In

600

Generator Power  In Generator Power  Out

Power (W)

500

400

300

200

100

0 0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

Input Speed (rpm)

Figure 37: Power versus Speed for the WindBlue Alternator Using 14.5:1 Gear Ratio (Experiment 4) – Maximum Uncertainty: ±5.97 W, ±0.012 rpm

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The results for Experiment 6 are shown in Figure 38. Due to the higher gearing ratio, an appropriate charging voltage was easily obtained. A maximum observed generator power output was approximately 350 W at an input speed of 15.6 rpm. The low cost model performed extremely well when using the 2 hp Nord gear motor and achieved a nontrivial power output. A larger range of speed inputs would have been explored if the motor had been capable of operating at greater than 60 Hz input frequency. 1800

Generator Power In

1600

Motor Power In 1400 Generator Power Out

Power (W)

1200

1000

800

600

400

200

0 0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

18.00

Input Speed (rpm)

Figure 38: Power versus Speed for the Delco-Remy Alternator Using 100:1 Gear Ratio (Experiment 6) – Maximum Uncertainty: ±3.02 W, ±0.003 rpm

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Figure 39 shows a summary of each generator’s efficiency as a function of input speed for Experiments 4, and 6. As the input speed is increased, the generator’s efficiency should reach a maximum point and then begin to drop again as frictional effects and heat loss begin to become dominant phenomena. If more data was able to be obtained (we were limited by maximum motor speed), this trend should exist. However, it is clear that there is a maximum efficiency of roughly 50% and 30% for the low cost and high performance models, respectively. 0.60

0.50

14.5:1 - Wind Blue 100:1 - Delco

Efficiency

0.40

0.30

0.20

0.10

0.00 0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

Input Speed (rpm)

Figure 39: Summary of Efficiencies for the WindBlue and Delco-Remy Generation Systems – Maximum Uncertainty: ±0.002, ±0.012 rpm

12. Technical Justification The purpose of this section is to detail why the team made certain design related decisions. Key decisions for both the low cost and high performance models will be outlined here. Additionally, the capabilities of a waterwheel will be estimated and applied to our experimental results.

12.1. Low­Cost Model Justification  The most important design decision regarding this model pertained to what gearing ratio was required to provide adequate speed input to the Delco-Remy car alternator. The rating information for this alternator stated that little to no electrical current will be generated until the alternator is spinning at a speed of 1000 rpm or greater. In order to estimate the required gearing ratio, the team needed to have some understanding of what the waterwheel input speed to the system would be. To do this, the team collected numerous waterwheel videos and timed the rotations of the wheel, both while under load and Formal Report Project: E45 – Personal Power Supply

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free spinning. An appropriate speed range obtained from this approximate analysis was 5 – 30 rpm. Therefore, the team chose an intermediate number of 15 rpm and a gearing ratio of approximately 100:1 to achieve an alternator speed of 1500 rpm. The team then selected a chain and sprocket – car flywheel and pinion combination to provide this ratio.

12.2. High­Performance Model Justification  Similar to the low cost model, the selection of appropriate gearing was the most critical decision for this design. However, the WindBlue permanent magnet alternator requires only a fraction of the speed input that the Delco-Remy requires, so a smaller gearing ratio should be used. Through the use of predicted performance curves provided by the manufacturer, it was estimated that the WindBlue permanent magnet alternator will produce 12 volts at approximately 250 rpm. This is sufficient for the team since we desire to power car components (car battery, headlights, fan, etc.) which all require about a 12 volt circuit. Therefore, using the estimated input speed of 15 rpm, a gearing ratio of approximately 16.7:1 is desired. However, to make our prototyping more modular, the team elected to use one portion of the low cost model’s gearing (car flywheel and pinion) to provide this ratio (14.5:1). While this does not quite meet the initial estimate, it provides the team with significant cost advantages and ease of assembly that will more than likely outweigh the disadvantages of a slight drop in speed.

12.3. Water Wheel Calculations  To determine the performance characteristics of a given waterwheel, the team would have liked to use an actual wheel and river, as this would have delivered the most reliable results. However, the design, acquisition, and testing of a waterwheel are not within the scope of this project. Instead, a suitable model to give a first order approximation of a waterwheel was used. The model chosen is called a Pelton Wheel, and all of the relating equations are from White’s Fluid Mechanics [Reference 2]. A simple schematic of a Pelton wheel is shown in Figure 40.

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Figure 40: Pelton water wheel [Reference 2]

The main assumptions associated with this model are: •

Constant river flow rate – In reality, the flow rate of a river will vary with season and time of day, but this assumption will allow at least for peak flow rate power output.

•

River flow behaves as a focused jet – The Pelton Wheel falls under the category of jet-impulse turbomachinery, and assumes a focused input. While a river will not actually provide this, it is believed that this model will still likely give adequate power estimates.

•

Beta = 110 degrees – This assumption was made to more adequately correlate the Pelton Wheel model to a simple waterwheel that will not likely have as large of paddle wheel curvature.

•

The governing equations describing the operating characteristics of the Pelton wheel are described here. The power output of the wheel is given by:

Where

is the water density, Q is the volumetric flow rate,

speed of the wheel, and

is the river velocity, u is the peripheral

is the paddle wheel curvature angle. The torque on the wheel can then be

calculated based on a basic power-speed relationship, namely:

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And lastly the efficiency can be calculated using the two relationships:

Where

is a dimensionless discharge coefficient (assumed to be 0.9) and

is the peripheral velocity

factor. In order to produce the expected performance curves for a Pelton Wheel, a river flow rate and wheel size must be assumed. Therefore a flow rate of 18 ft/s was used to generate plots for wheel diameters of: 3.3 ft, 9.8 ft, and 14.9 ft. The power, torque, and efficiency curves are shown in Figure 41, Figure 42, and Figure 43, respectively.

Figure 41: Power curves of Pelton water wheels

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Figure 42: Torque curves of Pelton water wheels on a logarithmic scale

Figure 43: Efficiency curves of Pelton water wheels

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From the above graphs, it is clear that typical trends for waterwheel are the following. For a given river flow rate: •

Power increases with an increase in wheel diameter

•

Torque increases with an increase in wheel diameter

•

Speed decreases with an increase in wheel diameter

This means that if smaller gearing ratios are desired, then smaller wheels should be used. However, the trade off will be that there will be a lower power input to the system. Through correlations to our experimental data, it was determined that the wheel that would best fit our results was the 3.3 ft (1 meter) wheel. This was because the smaller wheel provided higher input speeds, which are required for our alternators. To determine an appropriate operating point, the torque versus speed curve for the Pelton Wheel was plotted along with the load torque versus speed curve based on our experimental results. The result for the low cost model is shown in Figure 44.

Figure 44: Operating point of Low-Cost model with Pelton water wheel

For the high performance model, the results of the Pelton Wheel did not correlate in the manner that the team would have desired. Essentially, the Pelton wheel seems to be under predicting the speed that a waterwheel will spin at while under load. The team feels that this is the case based on the numerous examples of waterwheels in use that we have observed through video documentation that spin faster than the speed suggested by the Pelton Wheel model. Therefore, it is important to note that the Pelton Wheel model is simply a first order approximation of how a waterwheel might perform. It should be expected that actual results deviate by 30% or more from the model’s predictions. Formal Report Project: E45 – Personal Power Supply

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The results of this analysis point out a critical point that must be taken into consideration during the implementation of a high performance Personal Power Supply: alternator speed and torque input are extremely critical, so the system’s gearing must be chosen appropriately. If it is believed that the waterwheel will not produce speeds upwards of 15 rpm or higher, then a larger gearing ratio must be used (larger than 14.5:1). This means either using a larger flywheel to pinion ratio, or adding another stage of gearing, as was done in the low cost model. Based on the results shown here, it is recommended to err on the side of caution and use a gearing ratio of 20:1 or higher for the high performance model.

12.4. General Considerations  Since waterwheel driven systems are typically very low speed, they usually very high torque. This means that consideration should be given as to the appropriate shaft size to use. For the system described above, the following design equations were used to ensure an appropriately sized shaft. It should be noted that the results shown here are a function of the power input and gearing used, so the result cannot be generalized to all situations. For each particular configuration, this calculation should be made to ensure a safe design. For a circular shaft under torsional loading, the torsional shear stress experienced by the shaft is given by:

In general, the maximum shear stress that a material can experience before failure is given as half the yield:

Additionally, to obtain the minimum required diameter a failure theory must be used. Since the loading of the shaft is mostly torsional, the maximum shear stress failure theory will be used. This theory can be expressed in the following manner:

, where F.S. is termed the factor of safety. For shaft design, a F.S. of equal to 2 should be sufficient. Combining the above shear stress relationships yields the following expression the minimum shaft diameter:

For AISI 1045 carbon steel and a 1hp input power, the required minimum diameter is

. A

diameter of 1in was used. See the appendix for a sample calculation of this value.

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12.5. Energy Cost Savings  In order to prove that the Personal Power Supply (PPS) can reduce the energy costs of a user, this simple study has been completed, comparing the energy cost of the Low-Cost Personal Power Supply with the energy cost from a utility. In Table 7, the Energy Cost is the average price of each kWh, both from the PPS (running at 350W) and from Wisconsin Utilities [10]. The WI Energy Cost per month is the price of energy with a continuous 350W consumption (the same as the PPS).

Personal Power Supply (PPS) Initial Investment Output Power Number of Hours per month* Energy Generated each month Maintenance Cost Energy Cost

$  250.00 0.350 720 252 $       5.00 $  0.0198

Wisconsin Utilities Wisconsin Energy Cost [10] WI Energy Cost per month

$  0.1235 USD/kWh $    31.12 USD

USD kW h/month kWh/month USD/month USD/kWh

*At 30 days/month Table 7: Energy cost calculations

From this information, it is possible to determine the user’s return on investment. In Figure 45, the energy cost from a utility is compared to the energy cost from the PPS. Since the PPS cost includes the initial investment, the graph shows that the PPS will save money for the user after 10 months.

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Figure 45: Energy cost comparison graph

13. Review of Specifications & Needs This section contains a review of the Product Specifications for each model, with arguments that demonstrate that these specifications have been met. By meeting these Product Specifications, the team may claim that the Customer Needs have also been met.

13.1. Low­Cost Model Performance  In order to demonstrate that the specifications have been (or may easily be) met for the Low-Cost Model, the specifications have been repeated in Table 8. Each specification is addressed in the order given by the table.

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Table 8: Low-Cost specifications

The Low-Cost prototype has been constructed such that a simple covering over the gearing stages and electrical components would protect the model from corrosion due to rain. The prototype was assembled without the use of heavy machinery and tooling. The specification was met when the personal power supply was constructed with basic hand tools such as wrenches and screw drivers, in a reasonable time span. During testing (Experiment 8), the team measured an electrical power output of 349.97W. This power output is sufficient for charging a battery quickly and safely. While charging the battery, the output voltage was regulated by the alternator to safely charge the battery without any unsafe over-voltage. The only maintenance required of the Low-Cost model is to lubricate the gearing systems regularly. In the United States, a quart of gear lubricant may be purchased for $4.79 [7]. One quart of this lubricant would be sufficient several months, which means that this specification has been met. In foreign countries, it would be difficult to know the prices or availability of lubrication. Although the team used machine tools to create more than five parts, the some of these parts may be replaced with parts that require no tooling. The team designed the prototype to be modular, in the interest of testing several configurations. A user attempting to construct one Personal Power Supply could more easily do so with five or less machined parts. The Website instructions contain information that is important when building the personal power supply including a high-level bill of materials, cost estimates, labor time, pictures and videos. At the data point where we measured the greatest output power, the alternator torque was calculated to be 3.53 ft-lb, or 4.78 N-m. This alternator torque is within our specified range. Finally, at the same data point referenced (maximum power output) the alternator speed was measured to be 1408 rpm. This speed is within our specified range. Thus, all of the specifications for the Low-Cost model have been met. Formal Report Project: E45 – Personal Power Supply

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13.2. High­Performance Model  In order to demonstrate that the specifications have been (or may easily be) met for the HighPerformance Model, the specifications have been repeated in Table 9. Each specification is addressed in the order given by the table.

Table 9: High-Performance specifications

The High-Performance prototype has been constructed such that a simple covering over the gearing stages and electrical components would protect the model from corrosion due to rain. The prototype was assembled without the use of heavy machinery and tooling. The specification was met when the personal power supply was constructed with basic hand tools such as wrenches and screw drivers, in a reasonable time span. During testing (Experiment 4), the team measured an electrical power output of 100.90W. This power output is sufficient for charging a battery quickly and safely. While charging the battery, the output voltage was regulated by the charge controller to safely charge the battery without any unsafe over-voltage. The only maintenance required of the High-Performance model is to lubricate the gearing system regularly. In the United States, a quart of gear lubricant may be purchased for $4.79 [7]. One quart of this lubricant would be sufficient several months, which means that this specification has been met. In foreign countries, it would be difficult to know the prices or availability of lubrication. On the High-Performance model, the user must machine a base for the alternator, a coupling for the pinion, and a coupling for the flywheel. Since these are the only parts requiring tooling, this specification has been met. The Website instructions contain information that is important when building the personal power supply including a high-level bill of materials, cost estimates, labor time, pictures and videos. At the data point where we measured the greatest output power, the alternator torque was calculated to be 3.03 ft-lb, or 4.11 N-m. This alternator torque is within our specified range. Formal Report Page 51 of 79 Project: E45 – Personal Power Supply Revision 1.0

Finally, at the same data point referenced (maximum power output) the alternator speed was measured to be 802.8 rpm. This speed is within our specified range. In Table 6, the team estimates the cost of the High-Performance model to be $501.75. Unfortunately, this is higher than the specification of $450. However, electrical components such as a charge controller or frequency inverter are expensive options that are not required to simply charge a battery. Without the charge controller, the cost is reduced to $360.21, which is within the specifications. Thus, all of the specifications for the High-Performance model have been met.

13.3. Original Problem  As previously discussed, the Product Specifications were developed as a measureable way to meet the identified Customer Needs. Since the Customer Needs are requirements for solving the Original Problem, and since the Product Specifications have been met, the team may claim that the two Personal Power Supply designs may be used to solve the Original Problem.

14. Costs & Economic Analysis This section contains a summary of all the cost, labor, and sales information relevant to this project. Detailed information on the product cost and labor requirements may be found in other sections of this report.

14.1. Project Cost  The design team was promised a $900 budget for completing the Personal Power Supply project. This budget was used for purchasing components for the prototypes. The $900 proposed was conservative, since the team assumed most parts would have to be purchased. Thanks to several generous donations from the team’s sponsors, the project was completed under budget.

14.2. Product Cost  The Bill of Materials for the two models (Table 5 and Table 6) includes the estimated product cost for each model. The product cost for each Personal Power Supply is as follows: $233.62 for the Low-Cost model, $501.75 for the High-Performance model. These costs depend greatly on the country in which the parts are purchased, as well as the condition of the parts.

14.3. Labor Requirement Summary  As discussed in the Manufacturing Documentation, the labor requirements for constructing the Personal Power Supplies are as follows: 10.75 hours for the Low-Cost model, 9.1 hours for the HighPerformance model. These time estimates assume a skilled machinist is performing each task. This means that other users may require more time for each task. Details about the labor requirements may be found in the Manufacturing Documentation.

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14.4. Sales Forecast  The original goal of this project is not to sell Personal Power Supplies. Rather, the goal is to share the team’s experiences with the world, in the hopes that anyone with some mechanical skills and motivation might be able to use our plans to assemble a Personal Power Supply successfully. For this reason, a sales forecast for this project would not be appropriate.

15. Standards, Compliance & Concerns Before concluding the Formal Report, it is necessary to include notes about practical concerns that have not previously been discussed. The most important concerns regard the safety aspects of constructing and operating the Personal Power Supply. The next concern is the environmental effect of the product. Other concerns addressed include applicable standards, regulatory compliance, and legal issues.

15.1. Safety Evaluation  To fully consider safety, both mechanical and electrical aspects of the project have to be considered in order to appropriately assess all potential hazard locations. The alternator, battery, charge controller, wiring and electrical loads utilized on our control board are all areas of potential shock hazard. All the electricity generated by the product is direct current (DC). The alternators are not fused, which creates an additional hazard in the event of a short circuit. This is why we recommend adding fuses to limit the risk of shock. The user must avoid touching the wiring of the generator circuit while the generator is spinning to avoid electric shock. Switching wires or adding wires when either model is in operation can be a potential shock hazard, as the alternator is producing a voltage and, potentially, a current if the battery or additional loads are hooked up. The safest way to work on the electrical system is by removing and securing the mechanical portions of the generator. In the mechanical system, the main safety concern for this project is rotating parts. The gearing stages on each respective product have potential pitch points where bodily harm or even death can occur if extreme caution and proper preparation protocol is not followed. Like any piece of machinery, there are locations that could cause bodily harm. Often, maintenance or modifications are attempted while the machine is operating, but this very dangerous to the user. In industry, proper procedures must be followed to ensure all power supplies to a respective piece of machinery are disabled. Guarding is the most simple and effective solution to these issues. Simply using a shelter to cover the entire system or using expanded metal and fasteners to cover the individual pinch points will effectively remove these potentially hazardous areas. The following procedure is recommended before performing any service or repairs to the Personal Power Supply: 1) Disable all potential motion by: (if necessary and if possible) a) Disengage main water wheel shaft from flow force. b) Use mechanical braking unit to counteract torque. c) Block all areas of motion with appropriate restricting devices. Formal Report Project: E45 – Personal Power Supply

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i)

Possible Devices: (1) Ratcheting come-along (2) Wood blocks (3) Ropes (4) Straps (a) These devices can be removed once servicing is complete. (i) Use caution when inserting and removing all devices. d) If motion cannot be stopped: i) Proceed to electrical device removal steps. ii) Motion may be difficult to stop if water is at peak flow rate. (1) Possibly due to flooding etc. 2) Disable electrical systems: a) Remove wiring for all components beyond the alternator. i) Remove battery, charge controller and main lines for all loads drawn off alternator. (1) Energy created now stopped at the wiring coming from alternator. (2) Be sure to avoid crossing alternator wires, as there is still energy at these points and could cause damage to the alternator by creating a short circuit between the two leads of the alternator. (3) Put wire nuts or electrical tape at the end of these wires and use cable ties to keep them out of the way of all other service that may need to be done to external electrical and mechanical hardware. b) Store battery in dry area. i) Prevent corrosion that could cause potential danger to the operator.

15.2. Environmental Impact Statement  Although this product was designed as a source for clean power, there are still minor environmental impacts caused by our personal electric generation system. One potential risk is the contamination of the river with grease used to lubricate the gears, chain, and bearings. This is only considered a small risk because of the viscosity of grease. Unlike oil, grease is thick and sticky which enables it to adhere to the gears and chain. To make sure that the river will not be contaminated, the Personal Power Supply should be enclosed to protect it from corrosion, and keep any contaminates from reaching the environment. The positive effects of this system greatly outweigh any of the negative impacts. In fact, the power output of the Low-Cost model (at 300W) running for one year would take 2.6 megawatt-hours off of the electrical grid. According to the U.S. Department of Energy, the average annual energy consumption of American house-holds in 2001 was 10.7 megawatt-hours [6]. The Personal Power Supply could potentially supply a quarter of this energy requirement for a single home. If used on a larger scale, this could greatly reduce the need for coal-fired power plants that pollute the environment.

15.3. Applicable Standards  The Personal Power Supply will not be sold or distributed to anyone. The purpose of the project is simply to provide instructions on how a user could build a personal power supply using a waterwheel. Formal Report Project: E45 – Personal Power Supply

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Therefore, any applicable standards that would apply to waterwheels and their locations in rivers would fall under the responsibility of the builder. In the case of the personal power supply, this design does not need to follow industry standards because each power supply will be uniquely constructed by the users, according to his or her needs. The builder of either of these personal power supplies should take care to follow the drawings and specifications detailed for each prototype. Appropriate engineering calculations have been completed in order to ensure proper sizing for all the given mechanical and electrical applications that exist within each model. It becomes the responsibility of the builder to perform and check calculations, should he/she choose to change any of the specifications of either model. Failure to do this could result in injury or death.

15.4. Regulatory Compliance  Since this generally means to comply with laws and regulations, replication of either of the personal power supplies will require adherence to all codes, laws and regulations in the particular country of application. Team P-Squared will not be held liable for any violation of these codes, laws and regulations as these models are product to be marketed for sale in the United States or other countries.

15.5. Legal Issues  For this project, legal issues such as patents will not be applicable to our design because the personal power supply will not be sold. The idea of using an alternator to transform mechanical energy from a waterwheel into electrical energy is not novel, and should not conflict with any patent restrictions. Each customer may use our instructions to construct personal power supply, but the user has the responsibility of ensuring that the assembly and use of their personal power supply complies with local laws and codes for all mechanical and electrical apparatus for both personal power supply designs.

16. Conclusions & Recommendations Since August 2008, Team P-Squared has been working rigorously to develop these models to become what they are today. The first phase entailed the developing ideas on paper and establishing a firm foundation for what our project and models were to become. The second phase took these ideas and concepts and brought them to life by developing our calculations and computer aided models into two physical prototypes. With the physical prototypes, design oversights were realized, as with any project, and then remedied with modifications and redesigns both before and during our testing process. With the design thoroughly solidified, the data gathered also came to this level. Proper testing equipment directly correlated with the success and validity of the recorded data. The final two designs met and exceed the customer requirements set forth at the outset of our project. During our interviews of customers we established very solid guidelines by which we were to design. The most significant of these, the customers felt, was the price point. In the market that we targeted for our low cost design there was little to no reliable power sources, along with little to no extra income to spend on a large power source. This included developing areas where any electricity would be welcome. We set forth the goal for our low cost design of 300 Watts of continuous power output at a cost Formal Report Project: E45 – Personal Power Supply

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of under $250. We estimated the scrap cost of our actual design to be $233, while supplying 350 Watts continuous power, both meeting our specifications. The high performance design came in just over our goal cost of $450, at scrap cost of $500. Additionally, we met our goal of 100 Watts continuous power output at a realistic input of under 60 rpm. Further changes could be made to our design in future iterations to help lower cost of both designs, and to improve overall performance. Although the low cost design already utilizes auto parts for all major stages, mounting could be made from scrap to lower the cost. Additionally, by utilizing used or salvaged bearings in combination with a lower current output alternator, the low cost design could save nearly 20% of total costs. The overall performance of the low cost design would not be compromised by these concessions because our alternator was already only achieving 17.8% of its maximum current. The high performance design has room for performance improvement in the electrical output. Right now our design is only able to output 18.75% of maximum current. This would be improved at a near linear rate with increased rotational speed. To achieve this additional gearing would be necessary, such as what was implemented in the low cost design. Due to the large torque requirements also required, a 100:1 gear ratio would be unrealistic and unnecessary. For instance, by doubling the gear ratio by increasing the size of flywheel, or by adding another gearing stage, the expected current output would also double. This simple change could bring the continuous power output to over 200 Watts without sacrificing mechanical performance or durability of our system. Costs could be reduced in this design by utilizing more salvaged auto parts. The charge controller was a large part of these costs and could also utilize a more simple design that would achieve the safety required, while not adding computer interfacing capability. Both designs would benefit in performance and cost with simple design changes. These changes could be implemented with minimal effort by anyone utilizing our website to create their own generator. Our website was created to achieve our goal of sharing our documents and designs with other groups and individuals who could benefit from our design. Throughout the semester we have documented our design process and results at muelectric.org. Through this website we were able to achieve our final goal of sharing this information with other people. We used Google software to provide our information in multiple languages in a place where it will live on long after we have completed our college careers.

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17. References [1] United States of America. U.S. Department of Energy. DETERMINING ELECTRIC MOTOR LOAD AND EFFICIENCY. [2] White, Frank M. Fluid mechanics. Boston: McGraw-Hill Higher Education, 2008. [3] McMaster-Carr. 23 Apr. 2009 . [4] "Shop for Flywheel at 1A Auto." 1A Auto: Aftermarket Auto Parts, Car Parts, Replacement Auto Body Parts, Truck Parts. 23 Apr. 2009 . [5] Speedy Metals. 23 Apr. 2009 . [6] "U.S. Household Electricity Data: A/C, Heating, Appliances." Energy Information Administration EIA - Official Energy Statistics from the U.S. Government. 25 Apr. 2009 . [7] "Kendall NS-MP Hypoid Gear Lubricant, 1 Qt SAE 80W-90 # 1043927 by Conoco Phillips." Aubuchon Hardware. 25 Apr. 2009 . [8] "MatWeb - The Online Materials Information Resource." Online Materials Information Resource MatWeb. 25 Apr. 2009 . [9] Figliola, Richard S., and Donald E. Beasley. Theory and Design for Mechanical Measurements. New York: Wiley, 2005. [10] "Electric Power Monthly - Average Retail Price of Electricity to Ultimate Customers by End-Use Sector, by State." Energy Information Administration - EIA - Official Energy Statistics from the U.S. Government. 28 Apr. 2009 .

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18. Appendix A: Experiment Data 18.1. Experiment 1 

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18.2. Experiment 2 

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18.3. Experiment 3 

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18.4. Experiment 4 

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18.5. Experiment 5 

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18.6. Experiment 6 

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18.7. Experiment 7 

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18.8. Experiment 8 

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18.9. Repeatability Data 

Note: NL means ‘no load’.

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19. Appendix B: Sample Calculations Three phase electrical input power:

Percent of Rated Motor Load:

Estimation of Motor Efficiency (curve fit from U.S. Dept. of Energy graph [1]):

= .37

Figure 46: Graph used to estimate input motor efficiency [1]

Mechanical Input Power:

Electrical Output Power:

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Motor Torque:

System Efficiency:

Uncertainty Calculations: Uncertainty for Power In:

Uncertainty for Power Out

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Uncertainty for Power In After Motor

Uncertainty for Efficiency of Generator

Waterwheel Calculations:

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20. Appendix C: Additional Machining & Assembly Instructions Special Concerns for Flywheel Hub and Coupling Due to the fact the flywheel hub and coupling required a significant amount of attention from the team, special, detailed instructions on how to implement them are given here. It should be noted that while these instructions are very specific, the general procedure can be applied to any car flywheel chosen for the system. Flywheel Hub Since the flywheel comes from an automobile, it requires some custom machining, fabrication and assembly work in order to ensure a precision end product. First, a piece of 6” diameter , ½” thick piece of AISI/SAE 1045 hot roll steel must be cut on steel saw. To cut a piece this thin, be sure to place jacks inside the saw chuck in order to prevent saw blade from being shattered. Without the jacks, too much vibration will occur at the cut area cause the blade to cut into areas not within the cut zone. Next a boss ring must be welded to the approximate center of the hub piece just cut. A boss ring is used as dummy that will be removed in the future after the necessary work on the lathe is complete. Indicate the outer diameter (O.D.) of the actual hub piece, NOT the boss ring. Get the indicator to within 0.001” per side. Setup proper tooling and take a face cut on the hub to clean up the face and ensure minimal grinding. Also, take a cut on the O.D. to clean up the perimeter of the hub. Attempt to clean up the back face of the hub if possible. This will create for less work on the grinder. Remove the piece from the lathe and cut the boss ring off with an abrasive wheel. Take the piece to the grinder and take off up to 0.002” at a time. Repeat this action on both sides of the hub until the face have 90% clean up value. Nominally, the center of mass occurs at the actual center of the flywheel. In order to keep the center of mass at this location, the inside of the flywheel should be covered with layout fluid so that a circular perimeter can be scribed on the flywheel at a size proportional to the hub diameter. Once the perimeter line has been scribed, place the hub within this perimeter to verify the size and location is accurate. After placement verified and approved, the flywheel and hub piece must have a light preheat prior to welding. This preheat ensures proper temperature for welding, especially the since the hub is made of 1045 steel, which requires a medium length preheat for all welding. Without this preheat, the integrity of the welds can become compromised due to the chemical makeup of the steel not receiving proper preparation, especially at the location of the welding fusion line. Take care NOT to overheat the flywheel, as it made of light gauge steel that is more susceptible to warping when heated since it is so thin. First, tack the hub to the diameter at four locations. Make sure proper welding settings are chosen and Stargon inert gas is utilized for shielding. Always place tack welds 180 degrees to each other to guarantee a symmetrical part within all geometric axes of consideration. After tacking, check that the hub has not shifted and then proceed to stitch weld the hub along the entire perimeter of the hub. Stitch welds are 1” to 1-1/2” long and there should be the same amount of non-welded area between each weld. Formal Report Page 71 of 79 Project: E45 – Personal Power Supply Revision 1.0

Allow the piece to cool and then the flywheel must be taken to the milling machine to have the mounting hole put into the hub. The flywheel MUST be trammed and indicated to ensure the exact hole center is located. The mass center of gravity has been achieved as best as possible, but the geometric center of flywheel and hub assembly must be located accurately in order to ensure the flywheel does not spin out of round. Properly fixture the flywheel in the milling machine and use a precision indicator in the machine head collett. Adjust along the x and y-axis until the best possible center can be found. Our flywheel was indicated to within ±0.002” on each and in each direction. Setup the readout on the milling machine for a six hole pattern, equal spacing (i.e. all at 60 degrees to each other). First drill with a pilot hole, using a drill bit size around 1/8”. The change out to the finish size drill bit of ½”. Recall that drill bits drill 0.005” oversize, so if a precision fit is desired then a smaller drill bit should be used and then the hole should be reamed to the appropriate size. For this application, a drill bit finish is not an issue. Flywheel Coupling The previously described flywheel hub is bolted onto this flywheel coupling, both of these parts are used on the high performance and low cost models. This piece has an O.D. of 6” at the flange and 15/8” at the hub. There is a 1” bore run through the entire length of the piece. To be economical, to pieces are made separately and then welded together in order to save on time and material costs. First, a 2-3/8” long piece of AISI/SAE 1045 cold finished round stock is cut on the saw. Recall, that actual length of the piece is 2-1/4”, but the extra 1/8” is provided for machining stock. Chuck this piece up and create piece as per drawing requirements. Make sure to machine 1/16” step on last ¼” of hub so its shoulder can be used as a positive stop for the flange to be pushed up against. Get finish sizes within 0.001” to ensure proper fit and line up for welding. Next a boss ring must be welded to the approximate center of the hub piece just cut. A boss ring is used as dummy that will be removed in the future after the necessary work on the lathe is complete. Indicate the O.D. of the actual hub piece, NOT the boss ring. Get the indicator to within 0.001” per side. Setup proper tooling and take a face cut on the hub to clean up the face and ensure minimal grinding. Also, take a cut on the O.D. to clean up the perimeter of the hub. Attempt to clean up the back face of the hub if possible. This will create for less work on the grinder. Next a boss ring must be welded to the approximate center of the hub piece just cut. A boss ring is used as dummy that will be removed in the future after the necessary work on the lathe is complete. Indicate the outer diameter (O.D.) of the actual hub piece, NOT the boss ring. Get the indicator to within 0.001” per side. Setup proper tooling and take a face cut on the hub to clean up the face and ensure minimal grinding. Also, take a cut on the O.D. to clean up the perimeter of the hub. Attempt to clean up the back face of the hub if possible. This will create for less work on the grinder. Place diameter 1-9/16” hole in the center of the hub as the final step. Remove the piece from the lathe and cut the boss ring off with an abrasive wheel. Take the piece to the grinder and take off up to 0.002” at a time. Repeat this action on both sides of the hub until the face have as close to as 100% clean up value as possible. Formal Report Project: E45 – Personal Power Supply

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After placement verified and approved, the flywheel and hub piece must have a medium preheat prior to welding. This preheat ensures proper temperature for welding, especially the since both the hub and flange pieces are made of 1045 steel, which requires a medium length preheat for all welding. Without this preheat, the integrity of the welds can become compromised due to the chemical makeup of the steel not receiving proper preparation, especially at the location of the welding fusion line. Take care NOT to overheat the flywheel, as it made of light gauge steel that is more susceptible to warping when heated since it is so thin. First, tack the hub to the diameter at four locations. Make sure proper welding settings are chosen and Stargon inert gas is utilized for shielding. Always place tack welds 180 degrees to each other to guarantee a symmetrical part within all geometric axes of consideration. After tacking, check that the hub has not shifted and then proceed to weld complete around the ENTIRE perimeter of the hub. After cooling, take assembled piece to milling machine and place six diameter ½” holes. Setup the readout on the milling machine for a six hole pattern, equal spacing (i.e. all at 60 degrees to each other). First drill with a pilot hole, using a drill bit size around 1/8”. The change out to the finish size drill bit of ½”. Recall that drill bits drill 0.005” oversize, so if a precision fit is desired then a smaller drill bit should be used and then the hole should be reamed to the appropriate size. For this application, a drill bit finish is not an issue.

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21. Appendix D: MATLAB Code for Water Wheel Calculations clear all clc %General Pelton design parameters Beta=110*(pi/180); ro=1000; Cv=0.9; %1.5 m/s jet velocity Vj1=1.5; Vj1=Cv*Vj1; %1.5 meter wheel D1=1.5; L1=0.25; W1=0.25; Aj1=L1*W1; n1_1=[0:0.001:Vj1/(2*pi*D1/2)]; u1_1=2*pi*(D1/2).*n1_1; P1_1=ro*Aj1*Vj1*u1_1.*(Vj1-u1_1)*(1-cos(Beta))*0.00134102209; n1_1=(60/(2*pi))*n1_1; T1_1=5252.*P1_1./n1_1; phi1_1=u1_1./(Vj1/Cv); eta1_1=2*(1-cos(Beta))*phi1_1.*(Cv-phi1_1); %3 meter wheel D2=3; L2=0.5; W2=0.5; Aj2=L2*W2; n2_1=[0:0.001:Vj1/(2*pi*D2/2)]; u2_1=2*pi*(D2/2).*n2_1; P2_1=ro*Aj2*Vj1*u2_1.*(Vj1-u2_1)*(1-cos(Beta))*0.00134102209; n2_1=(60/(2*pi))*n2_1; T2_1=5252.*P2_1./n2_1; phi2_1=u2_1./(Vj1/Cv); eta2_1=2*(1-cos(Beta))*phi2_1.*(Cv-phi2_1); %4.5 meter wheel D3=4.5; L3=0.75; W3=0.75; Aj3=L3*W3; n3_1=[0:0.001:Vj1/(2*pi*D3/2)]; u3_1=2*pi*(D3/2).*n3_1; P3_1=ro*Aj3*Vj1*u3_1.*(Vj1-u3_1)*(1-cos(Beta))*0.00134102209; n3_1=(60/(2*pi))*n3_1; T3_1=5252.*P3_1./n3_1; phi3_1=u3_1./(Vj1/Cv); eta3_1=2*(1-cos(Beta))*phi3_1.*(Cv-phi3_1); %2.5 m/s jet velocity Vj2=2.5; Vj2=Cv*Vj2; %1.5 meter wheel

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n1_2=[0:0.001:Vj2/(2*pi*D1/2)]; u1_2=2*pi*(D1/2).*n1_2; P1_2=ro*Aj1*Vj2*u1_2.*(Vj2-u1_2)*(1-cos(Beta))*0.00134102209; n1_2=(60/(2*pi))*n1_2; T1_2=5252.*P1_2./n1_2; phi1_2=u1_2./(Vj2/Cv); eta1_2=2*(1-cos(Beta))*phi1_2.*(Cv-phi1_2); %3 meter wheel n2_2=[0:0.001:Vj2/(2*pi*D2/2)]; u2_2=2*pi*(D2/2).*n2_2; P2_2=ro*Aj2*Vj2*u2_2.*(Vj2-u2_2)*(1-cos(Beta))*0.00134102209; n2_2=(60/(2*pi))*n2_2; T2_2=5252.*P2_2./n2_2; phi2_2=u2_2./(Vj2/Cv); eta2_2=2*(1-cos(Beta))*phi2_2.*(Cv-phi2_2); %4.5 meter wheel n3_2=[0:0.001:Vj2/(2*pi*D3/2)]; u3_2=2*pi*(D3/2).*n3_2; P3_2=ro*Aj3*Vj2*u3_2.*(Vj2-u3_2)*(1-cos(Beta))*0.00134102209; n3_2=(60/(2*pi))*n3_2; T3_2=5252.*P3_2./n3_2; phi3_2=u3_2./(Vj2/Cv); eta3_2=2*(1-cos(Beta))*phi3_2.*(Cv-phi3_2); %3.5 m/s jet velocity Vj3=3.5; Vj3=Cv*Vj3; %1.5 meter wheel n1_3=[0:0.001:Vj3/(2*pi*D1/2)]; u1_3=2*pi*(D1/2).*n1_3; P1_3=ro*Aj1*Vj3*u1_3.*(Vj3-u1_3)*(1-cos(Beta))*0.00134102209; n1_3=(60/(2*pi))*n1_3; T1_3=5252.*P1_3./n1_3; phi1_3=u1_3./(Vj3/Cv); eta1_3=2*(1-cos(Beta))*phi1_3.*(Cv-phi1_3); %3 meter wheel n2_3=[0:0.001:Vj3/(2*pi*D2/2)]; u2_3=2*pi*(D2/2).*n2_3; P2_3=ro*Aj2*Vj3*u2_3.*(Vj3-u2_3)*(1-cos(Beta))*0.00134102209; n2_3=(60/(2*pi))*n2_3; T2_3=5252.*P2_3./n2_3; phi2_3=u2_3./(Vj3/Cv); eta2_3=2*(1-cos(Beta))*phi2_3.*(Cv-phi2_3); %4.5 meter wheel n3_3=[0:0.001:Vj3/(2*pi*D3/2)]; u3_3=2*pi*(D3/2).*n3_3; P3_3=ro*Aj3*Vj3*u3_3.*(Vj3-u3_3)*(1-cos(Beta))*0.00134102209; n3_3=(60/(2*pi))*n3_3; T3_3=5252.*P3_3./n3_3; phi3_3=u3_3./(Vj3/Cv); eta3_3=2*(1-cos(Beta))*phi3_3.*(Cv-phi3_3); %4.5 m/s jet velocity Vj4=4.5; Vj4=Cv*Vj4; %1.5 meter wheel

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n1_4=[0:0.001:Vj4/(2*pi*D1/2)]; u1_4=2*pi*(D1/2).*n1_4; P1_4=ro*Aj1*Vj4*u1_4.*(Vj4-u1_4)*(1-cos(Beta))*0.00134102209; n1_4=(60/(2*pi))*n1_4; T1_4=5252.*P1_4./n1_4; phi1_4=u1_4./(Vj4/Cv); eta1_4=2*(1-cos(Beta))*phi1_4.*(Cv-phi1_4); %3 meter wheel n2_4=[0:0.001:Vj4/(2*pi*D2/2)]; u2_4=2*pi*(D2/2).*n2_4; P2_4=ro*Aj2*Vj4*u2_4.*(Vj4-u2_4)*(1-cos(Beta))*0.00134102209; n2_4=(60/(2*pi))*n2_4; T2_4=5252.*P2_4./n2_4; phi2_4=u2_4./(Vj4/Cv); eta2_4=2*(1-cos(Beta))*phi2_4.*(Cv-phi2_4); %4.5 meter wheel n3_4=[0:0.001:Vj4/(2*pi*D3/2)]; u3_4=2*pi*(D3/2).*n3_4; P3_4=ro*Aj3*Vj4*u3_4.*(Vj4-u3_4)*(1-cos(Beta))*0.00134102209; n3_4=(60/(2*pi))*n3_4; T3_4=5252.*P3_4./n3_4; phi3_4=u3_4./(Vj4/Cv); eta3_4=2*(1-cos(Beta))*phi3_4.*(Cv-phi3_4); %5.5 m/s jet velocity Vj5=5.5; Vj5=Cv*Vj5; %1.5 meter wheel n1_5=[0:0.001:Vj5/(2*pi*D1/2)]; u1_5=2*pi*(D1/2).*n1_5; P1_5=ro*Aj1*Vj5*u1_5.*(Vj5-u1_5)*(1-cos(Beta))*0.00134102209; n1_5=(60/(2*pi))*n1_5; T1_5=5252.*P1_5./n1_5; phi1_5=u1_5./(Vj5/Cv); eta1_5=2*(1-cos(Beta))*phi1_5.*(Cv-phi1_5); %3 meter wheel n2_5=[0:0.001:Vj5/(2*pi*D2/2)]; u2_5=2*pi*(D2/2).*n2_5; P2_5=ro*Aj2*Vj5*u2_5.*(Vj5-u2_5)*(1-cos(Beta))*0.00134102209; n2_5=(60/(2*pi))*n2_5; T2_5=5252.*P2_5./n2_5; phi2_5=u2_5./(Vj5/Cv); eta2_5=2*(1-cos(Beta))*phi2_5.*(Cv-phi2_5); %4.5 meter wheel n3_5=[0:0.001:Vj5/(2*pi*D3/2)]; u3_5=2*pi*(D3/2).*n3_5; P3_5=ro*Aj3*Vj5*u3_5.*(Vj5-u3_5)*(1-cos(Beta))*0.00134102209; n3_5=(60/(2*pi))*n3_5; T3_5=5252.*P3_5./n3_5; phi3_5=u3_5./(Vj5/Cv); eta3_5=2*(1-cos(Beta))*phi3_5.*(Cv-phi3_5);

%Plots for 1.5 m/s flow rate %Power figure(1)

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clf plot(n1_1,P1_1,'g-',n2_1,P2_1,'b-',n3_1,P3_1,'r-') title('Power of Pelton Wheel as a Function of Rotational Speed for River Speed of 4.9 ft/s') xlabel('Wheel Rotational Speed (rpm)') ylabel('Power Output (hp)') legend('4.9 ft Diameter Wheel','9.8 ft Diameter Wheel','14.8 ft Diamter Wheel') %Torque figure(2) clf semilogy(n1_1,T1_1,'g-',n2_1,T2_1,'b-',n3_1,T3_1,'r-') title('Torque Provided by Pelton Wheel as a Function of Rotational Speed for River Speed of 4.9 ft/s') xlabel('Wheel Rotational Speed (rpm)') ylabel('Torque (ft-lbs)') legend('4.9 ft Diameter Wheel','9.8 ft Diameter Wheel','14.8 ft Diamter Wheel') %Efficiency figure(3) clf plot(n1_1,eta1_1,'g-',n2_1,eta2_1,'b-',n3_1,eta3_1,'r-') title('Efficiency of Pelton Wheel as a Function of Rotational Speed for River Speed of 4.9 ft/s') xlabel('Wheel Rotational Speed (rpm)') ylabel('Efficiency (-)') legend('4.9 ft Diameter Wheel','9.8 ft Diameter Wheel','14.8 ft Diamter Wheel') %Plots for 2.5 m/s flow rate %Power figure(4) clf plot(n1_2,P1_2,'g-',n2_2,P2_2,'b-',n3_2,P3_2,'r-') title('Power of Pelton Wheel as a Function of Rotational Speed for River Speed of 8.2 ft/s') xlabel('Wheel Rotational Speed (rpm)') ylabel('Power Output (hp)') legend('4.9 ft Diameter Wheel','9.8 ft Diameter Wheel','14.8 ft Diamter Wheel') %Torque figure(5) clf semilogy(n1_2,T1_2,'g-',n2_2,T2_2,'b-',n3_2,T3_2,'r-') title('Torque Provided by Pelton Wheel as a Function of Rotational Speed for River Speed of 8.2 ft/s') xlabel('Wheel Rotational Speed (rpm)') ylabel('Torque (ft-lbs)') legend('4.9 ft Diameter Wheel','9.8 ft Diameter Wheel','14.8 ft Diamter Wheel') %Efficiency figure(6) clf plot(n1_2,eta1_2,'g-',n2_2,eta2_2,'b-',n3_2,eta3_2,'r-') title('Efficiency of Pelton Wheel as a Function of Rotational Speed for River Speed of 8.2 ft/s')

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xlabel('Wheel Rotational Speed (rpm)') ylabel('Efficiency (-)') legend('4.9 ft Diameter Wheel','9.8 ft Diameter Wheel','14.8 ft Diamter Wheel') %Plots for 3.5 m/s flow rate %Power figure(7) clf plot(n1_3,P1_3,'g-',n2_3,P2_3,'b-',n3_3,P3_3,'r-') title('Power of Pelton Wheel as a Function of Rotational Speed for River Speed of 11.5 ft/s') xlabel('Wheel Rotational Speed (rpm)') ylabel('Power Output (hp)') legend('4.9 ft Diameter Wheel','9.8 ft Diameter Wheel','14.8 ft Diamter Wheel') %Torque figure(8) clf semilogy(n1_3,T1_3,'g-',n2_3,T2_3,'b-',n3_3,T3_3,'r-') title('Torque Provided by Pelton Wheel as a Function of Rotational Speed for River Speed of 11.5 ft/s') xlabel('Wheel Rotational Speed (rpm)') ylabel('Torque (ft-lbs)') legend('4.9 ft Diameter Wheel','9.8 ft Diameter Wheel','14.8 ft Diamter Wheel') %Efficiency figure(9) clf plot(n1_3,eta1_3,'g-',n2_3,eta2_3,'b-',n3_3,eta3_3,'r-') title('Efficiency of Pelton Wheel as a Function of Rotational Speed for River Speed of 11.5 ft/s') xlabel('Wheel Rotational Speed (rpm)') ylabel('Efficiency (-)') legend('4.9 ft Diameter Wheel','9.8 ft Diameter Wheel','14.8 ft Diamter Wheel') %Plots for 4.5 m/s flow rate %Power figure(10) clf plot(n1_4,P1_4,'g-',n2_4,P2_4,'b-',n3_4,P3_4,'r-') title('Power of Pelton Wheel as a Function of Rotational Speed for River Speed of 14.8 ft/s') xlabel('Wheel Rotational Speed (rpm)') ylabel('Power Output (hp)') legend('4.9 ft Diameter Wheel','9.8 ft Diameter Wheel','14.8 ft Diamter Wheel') %Torque figure(11) clf semilogy(n1_4,T1_4,'g-',n2_4,T2_4,'b-',n3_4,T3_4,'r-') title('Torque Provided by Pelton Wheel as a Function of Rotational Speed for River Speed of 14.8 ft/s') xlabel('Wheel Rotational Speed (rpm)') ylabel('Torque (ft-lbs)')

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legend('4.9 ft Diameter Wheel','9.8 ft Diameter Wheel','14.8 ft Diamter Wheel') %Efficiency figure(12) clf plot(n1_4,eta1_4,'g-',n2_4,eta2_4,'b-',n3_4,eta3_4,'r-') title('Efficiency of Pelton Wheel as a Function of Rotational Speed for River Speed of 14.8 ft/s') xlabel('Wheel Rotational Speed (rpm)') ylabel('Efficiency (-)') legend('4.9 ft Diameter Wheel','9.8 ft Diameter Wheel','14.8 ft Diamter Wheel') %Plots for 5.5 m/s flow rate %Power figure(13) clf plot(n1_5,P1_5,'g-',n2_5,P2_5,'b-',n3_5,P3_5,'r-') title('Power of Pelton Wheel as a Function of Rotational Speed for River Speed of 18.0 ft/s') xlabel('Wheel Rotational Speed (rpm)') ylabel('Power Output (hp)') legend('4.9 ft Diameter Wheel','9.8 ft Diameter Wheel','14.8 ft Diamter Wheel') %Torque figure(14) clf semilogy(n1_5,T1_5,'g-',n2_5,T2_5,'b-',n3_5,T3_5,'r-') title('Torque Provided by Pelton Wheel as a Function of Rotational Speed for River Speed of 18.0 ft/s') xlabel('Wheel Rotational Speed (rpm)') ylabel('Torque (ft-lbs)') legend('4.9 ft Diameter Wheel','9.8 ft Diameter Wheel','14.8 ft Diamter Wheel') %Efficiency figure(15) clf plot(n1_5,eta1_5,'g-',n2_5,eta2_5,'b-',n3_5,eta3_5,'r-') title('Efficiency of Pelton Wheel as a Function of Rotational Speed for River Speed of 18.0 ft/s') xlabel('Wheel Rotational Speed (rpm)') ylabel('Efficiency (-)') legend('4.9 ft Diameter Wheel','9.8 ft Diameter Wheel','14.8 ft Diamter Wheel')

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