2008 Human Powered Vehicle

Transcription

1 Portland State University Maseeh College of Engineering and Computer Science 2008 Human Powered Vehicle Progress Report Winter 2008 March 12 th, 2008 PSU Advisor: Team: Derek Tretheway Ben Bolen Erik Chamberlain Kenneth Lou Levi Patton Bryan Voytilla

2 Executive Summary The 2008 Portland State University Human Powered Vehicle design team has designed and is constructing an HPV for use by the PSU HPV race team in the ASME Western Region HPV Challenge. The PSU HPV design team set design criteria based on past experience in the HPVC and external research. The goal of these criteria is to produce an HPV that enables the PSU HPV race team to win the HPVC. A rear wheel drive recumbent bicycle, with an adjustable boom, a fixed seat, and a full fairing was designed. This configuration was selected because it provided the highest performance based on design criteria with the fewest compromises. A bicycle was selected to provide stability at high speeds. The rear wheel drive train enables the HPV to achieve top speed prescribed by design criteria; which were unachievable with a front wheel drive configuration. A fixed seat and adjustable boon configuration was selected for minimum time requirement during rider change. These design criteria come with inherent drawbacks. A rear wheel drive train requires the routing of the chain from the front driven sprocket to the rear drive sprocket. It also suffers from inefficiency caused by the lengthened chain. The bicycle configuration while stable at high speed is unstable at low speeds. These compromises were deemed acceptable because of their performance benefits. Fabrication has begun on the PSU HPV and the ASME HPVC design report is being written. The fabrication of the PSU HPV is 85% complete and the ASME design report is 50% complete. Both items are on track to be completed on time and under budget. The 2008 PSU HPV will provide the PSU HPV race team a vehicle that is capable of winning the ASM Western Region Challenge. 1

3 Table of Contents Executive Summary... 1 Introduction... 3 Mission statement... 3 Latest project planning document... 3 Final PDS summary... 4 External search... 5 Internal search... 7 Top-level final design evaluation and Selection Progress on detailed design Conclusion and Recommendations Appendix A: Product Design Specifications Appendix B: Frame Configuration Appendix C: Fairing Material Selection Appendix D: Drive Train Configuration Appendix E: Turning Analysis Appendix F: Fairing configuration Appendix G: Straight line aerodynamic efficiency Appendix H: Finite Elemental Analysis Appendix I: Biomechanical Testing Appendix J: Vehicle Stability Appendix K: Top Speed Analysis Appendix L: Budget Appendix M: Ergonomics

4 Introduction The American Society of Mechanical Engineers (ASME) holds Human Powered Vehicle Competitions (HPVCs) each April at host schools on the west coast. HPVCs are a way for mechanical engineering students to practice their design skills and get hands on experience in fabricating a vehicle. Teams are judged in three categories; vehicle design, a 100m sprint race, and a 60km endurance race. The Portland State University (PSU) Human Powered Vehicle (HPV) capstone design team (or team, for short) is building an HPV, nicknamed Vike Bike I. This report overviews the overall team mission, project timeline, and main product design specifications (see Appendix A for all the high, medium, and low priority specifications from the PDS document). The most relevant existing products for each of the vehicle sub-functions are discussed and evaluated. Five integrated concepts that were developed by team brainstorming are presented and compared to select the final Vike Bike I design. Detailed design progress is provided, as well as a summary of what has been completed so far. This report concludes with future work and milestones to be achieved. The appendices contain the as well as documentation of detailed design analyses. Mission statement Portland State University s HPV capstone design team aims to develop an innovative, lightweight, and aerodynamic HPV for the PSU HPV Race Team to win the overall ASME Western Region HPV Competition on 18 April The Vike Bike I must be within budgetary constraints and conform to the rules overseen by the HPVC judges. Completed on or before the 4 th of April 2008 so that the Race Team will have time test and modify (if needed) the vehicle. Latest project planning document The majority of the project timeline has been set by the HPV design team. However, the report and administrative dates are largely controlled by ASME and the ME 492/93 Capstone sequence. Other task completion dates and periods have been set to meet these goals. Figure 1 (below) gives the current schedule for the completion of various tasks. 3

5 Figure 1: Project timeline as of 11 March Tough constraints with the timeline provide for strict guideline and a very time consuming project. Along with the production for competition of the Vike Bike I, documentation must also be provided with detailed design specifications describing the different criterion in which the design is based. Final PDS summary The Product Design Specifications document defines the mission statement of the project, a project plan containing milestones for task completion, identifies the internal and external customers, the criteria used in designing the HPV, and a house of quality quantifying customer needs. The PDS is used to asses customer needs, timeline, and priority of design specifications. A summary of product design specifications is given in Table 1; the full text of the PDS report can be found in Appendix A. 4

6 Table 1: Summary of highest priority product design specifications. Criteria: Performance Requirements Primary Customer Top speed PSU-HPV Team Top speed in male and female sprint races Strength ASME HPVC Judges Measurement Metric Target Target Basis Verification Method Frame safety factor Crash recovery PSU-HPV Team Time to selfupright High-speed stability PSU-HPV Team Vehicle does not wobble uncontrollably at straight line speeds > 20mph Straight line aerodynamic efficiency Partial fairing removal for rider entry and exit HPV needs to last through construction, testing, and HPV Challenge. mph >45 mph Competition research Nondimensional PSU-HPV Team Coefficient of drag Nondimensional PSU-HPV Team Rider change out time >1.5 Competition research Seconds < 15s Competition research Steering axis < 5deg Competition rotation in research degrees <=.14 Frontal area is an improvement upon Vike Trike II fairing Seconds <60s Improve upon Vike Trike II fairing Life In Service PSU-HPV Team Life of bike Months > April 2008 Stay under budget PSU-HPV Team Stay under budget with material and fabrication cost Cost Rider Safety Visibility PSU-HPV Team Visibility Degrees of vertical and horizontal view Strength PSU-HPV Team Fairing strength Flexure modulus Bike must last until HPV Challenge is over Dollars > Budget Competition research Horizontal > 150 degrees Vertical > 60 degrees >= 2007 PSU HPV fairing Rider preference Competition research Vehicle Time trial research Design analysis Vehicle testing Vehicle testing Theoretical verification with CFD and achieved with wind tunnel testing Time trial testing Inspection Expenditure accounting Measurement Materials testing External search An external search was conducted to investigate possible preexisting design solutions for various HPV sub-projects. These solutions come from the Vike Trike I, the Vike Trike II team, and external organizations. The results of this search are given below. A standard real wheel drive (RWD) setup was examined for the Vike Bike I drive train. This setup has the advantage of using commercial availability components to ease the manufacturing 5

7 process. Chain routing and efficiency are intrinsic to this type of arrangement. Commercially available gears were analyzed for potential use in the Vike Bike I. This option requires little manufacturing but is limited to the sizes of commercially available gears. The frame of Vike Trike II was examined for design ideas involving chain routing, drive train, safety, ergonomics, and practicality of manufacturing. These designs were successful in last year s HPVC. The weight of the frame can be reduced by optimizing material selection. The fairings of the Vike Trike I and II were examined to determine its positive and negative aerodynamic and material properties. National Advisory Committee for Aeronautics (NACA) shapes were studied and used to determine aerodynamic characteristics of various fairing designs. The Cobra Bikes steering mechanism offers easy rider change out, good range of motion, but might not be as intuitive to use as standard dropdown handlebars mounted directly over the fork. The adjustable boom of the Vike Trike II was studied and has the advantage of quick adjustability and a permanently mounted rider seat allows for a large range of adjustability to account for discrepancy in rider height. Disc brakes were considered for use in stopping the Vike Bike I. Disc style brakes have the advantage of high stopping force, and the exposure to the ambient air allows for convective cooling. They are commercially available, and are easily mounted to commercially available hubs. Commercially available SRAM road style shifters were chosen for use on the Vike Bike I for ergonomic purposes. 6

8 Internal search In the initial design stage of the Vike Bike I each team member brainstormed for their ideal HPV. Five concepts were developed varying from a two wheeled upright bicycle to a virtual HPV. Concept 1 One integrated concept is to use a short wheelbase, recumbent, bike, with rear wheel drive, an adjustable boom, a fixed seat, and a fully enclosed torpedo-shaped fairing with landing gear that will be used in the endurance and sprint races (see Figure 2, below). Figure 2: Sketch of Concept 1 Concept 2 This concept is based off of the common upright diamond framed bicycle sold in many bicycle shops. The concept has front wheel steering and rear wheel drive, with the rider seated in the upright position in an adjustable seat which compensates for different rider sizes (sees Figure 3, below). To satisfy the ASME competition rules the concept will utilize a partial fairing for both endurances and sprint races. Figure 3: Sketch of Concept 1 7

9 Concept 3 Another concept would be a continuation of the Vike Trike II HPV with improved fairing design, high speed stability, and drive train efficiency (see Figure 4, below). It should have three wheels and be rear wheel drive. The seat should be fixed and the boom should be adjustable. The focus will be on refining existing sub-systems rather than innovating new solutions. Figure 4: Sketch of concept 3 Concept 4 The fourth concept integrates a fully-faired, recumbent, tadpole trike with RWD (see Figure 5 and Figure 6, below). Visibility is achieved via an integrated video system. The rider is positioned with their head at the front of the vehicle to reduce chain routing and frontal area. The riding position is not prone, merely backwards. Accommodation for different size riders is done with an adjustable seat. Direction of travel Figure 5: Top view of concept 4 8

10 Video camera Video glasses Figure 6: Side view of concept 4 Concept 5 Concept 5 integrates Long wheelbase, two sided FWD, pedals turn with front wheel, recumbent bicycle, large gears, adjustable boom, low center of gravity, carbon frame, fully faired for sprint and endurance race (see Figure 7 and Figure 8, below). The steering being attached to the pedals will help aid in the spring allowing the rider to pull up on the handlebars as they push down on the pedals simulating a sprint on an upright bicycle. Figure 7: Drive Train for concept 5 Figure 8: Side view of concept 5 9

11 Top-level final design evaluation and Selection The concepts listed above were evaluated in a concept scoring matrix (see Table 2, below), using the Vike Trike II as a datum. Scoring is from a 1-5 range, with scores meaning: 1 Very inferior 2 Inferior 3 Acceptable 4 Superior 5 Much superior Table 2: Concept scoring matrix Datum Concept 1 Concept 2 Concept 3 Concept 4 Concept 5 Performance Top speed Frame Strength Crash recovery High-speed stability Straight line aerodynamic efficiency Partial fairing removal for rider entry and exit Cost Stay under budget Life in Service HPV to last through construction, testing, and competition Rider Safety Visibility Fairing Strength Total Score Concept 1 is nine points above the datum, and six points above the nearest competitor. Each of the ten main design requirements is given equal weight in this scoring matrix, so the minimum possible score is ten points and a maximum possible score is 50 points. Dividing the total score by the number of requirements gives an average score range of one through five. This is convenient because the same scoring range listed above can be used. Therefore, Concept 1 is very close to a superior rating. Likewise, Concepts 2, 3, and 5 are close to an acceptable rating and Concept 4 is half way between poor and average. 10

12 The concept scoring matrix clearly indicates that team will be manufacturing Concept 1: the short wheelbase, recumbent, bike, with rear wheel drive, an adjustable boom, a fixed seat, and a fully enclosed torpedo-shaped fairing with landing gear to be used in the endurance and sprint races. With a commitment to working on Concept 1, each of the product sub-functions requires detailed design decisions beyond the top-level concepts. Progress on detailed design Detailed design was initiated from the top-level concept selection. Specific components were selected or designed based off of the PDS requirements. To achieve the required top speed of over 45mph, the final design uses a 75 tooth chain ring and a standard 10 speed cassette on the rear wheel (see Appendix E). Taking air drag, rolling resistance, and rider power output into account, Vike Bike I should be able to reach a maximum speed of 55 mph (see Appendix N). Top speed was increased by decreasing rolling resistance through weight reduction (see Appendix I) and decreasing the drag force (see Appendix H). Top speed verification will be obtained through time-trial testing the vehicle, once construction is completed. The requirement of improving straight-line aerodynamic efficiency will be verified by computational fluid dynamics (CFD) and wind tunnel testing. To achieve the required braking distance of 15ft at 20mph, disc brakes will be used for the front wheel, and caliper brakes will be used for the rear wheel. Since disc brakes can apply more braking force than caliper brakes, the risk of vehicle tip forward will need to be analyzed. Vehicle testing will be used to verify the braking distance at the specified speed. The frame will not fail in top, side, or dynamic loading. Finite Elemental Analysis shows a minimum factor of safety of 1.5, which occurs under the ASME side load situation. Tube dimensions and FEA analysis are located in Appendix J. Material properties used in the FEA analysis will be verified with materials testing. 11

13 A retractable flap system will be used so that the riders can upright themselves during the event of a crash. Testing of the completed bike assembly will consist of putting the bike on its side, and timing how long it takes for the riders to upright themselves. The 2008 PSU HPV is required to have a minimum turning radius of 25ft as stated by the ASME rules. An analysis was performed to ensure that the HPV conformed to the ASME steering requirement. This analysis, presented in appendix F, took into consideration the worst case scenario of no bike lean so that the turning radius is completely dependent on steering geometry. The stability of a recumbent bike depends on its wheel base. The longer the wheelbase and trail the more stable the bike. The general rule is a trail of more than 3.5 and a wheelbase larger than 60 leads to stability while trail and wheelbases shorter lead to instability. For a given power output by a rider reducing the aerodynamic drag force which will give the HPV a higher velocity. The two variables manipulated by the design team that contribute to aerodynamic efficiency are coefficient of drag and frontal area. To date it is shown that the frontal area of the 2008 HPV fairing is reduced when compared to the 2006 HPV fairing. This reduction in frontal area will contribute to the overall reduction in drag force. A verification of this reduction in frontal area is performed in appendix G. A Finite element analysis (FEA) was performed to analyze stress, strain, displacement, modal frequency and weight of the Vike Bike I frame. The tube dimensions were optimized to minimum weight while maintaining the required factor of safety of at least 1.5 against the ASME HPVC prescribed load conditions. Future work for FEA includes finding strain and displacement for ASME rules compliance (see appendix H). FEA will be verified through strain gauge testing. 12

14 Ergonomic dimension for Vike Bike I were based off of Vike Trike II who s angles were determined based optimal power output for recumbent cycling (Furniss, Kappa, Smith, Stenkamp, Tavan, 2007). Conclusion and Recommendations Conceptual Design One was selected for use in the 2008 PSU HPV. The Vike Bike I is a recumbent bicycle that features a short wheelbase, recumbent riding position, rear wheel drive, an adjustable boom, a fixed seat, is fully faired in the endurance and sprint race, has a torpedo shaped fairing. The fairing is designed based on the NACA II fairing shape and is symmetrical both top and bottom and side to side. Frame material selection and tube sizing was done with a FEA model. Aluminum was selected for use in the frame based on its strength to weight ratio, and an optimization was performed to determine the lowest possible tube sizes while maintaining the required safety factor of 1.5. Optimal power angles were determined based on external research involving human pedaling performance. Gears were selected based on calculations that assumed a maximum speed of 45 mph and took into account the power riders were able to achieve during biomechanical testing, rolling resistance, and aerodynamic drag. Milestones achieved thus far include the PDS report submitted February 4 th, 2008, competition registration, 85% completion of frame and fairing manufacturing, and 80% completion on the ASME HPVC design report due on 17 February All tasks are on track to be complete on time, but the fairing mold and frame tube notching are behind schedule. The design produced exceeds all required factors of safety set by the ASME HPVC. It also theoretically provides performance in excess of all goals specified by the team. Physical testing for these performance criteria will be conducted upon HPV completion. A compromise was made in selecting a rear wheel drive train. This was done because a front wheel drive train could not provide speed specified in the design criteria and was more difficult to design. Rear wheel drive adds the complication of chain routing and decreased efficiency due to the 13

15 increased length in chain. A compromise was also made in HPV tube sizes. The sizes are limited to standard commercially bendable diameters and wall thickness. This increased the overall weight of the HPV but made possible accurate bending done by a PSU HPV team sponsor. Appendix A: Product Design Specifications Important sections from the PDS document are reproduced in this Appendix. These sections are the introduction, document explanation, identification of customers, customer feedback, product design specifications, house of quality, and conclusion. Introduction The American Society of Mechanical Engineers (ASME) Human Powered Vehicle (HPV) Challenge is a competition in which engineering students from around the country design, construct, and race an HPV. An HPV can take many forms and varying rider positions, such as upright, recumbent, or prone and can have any number of wheels. The competition consists of three separate events: a 100m sprint race, a 60km grand prix style endurance race, and a judging process for the vehicle s design, safety, and formal presentation. Because of increasing energy prices and growing concern over vehicle pollution, the HPV Challenge was created to encourage development in human powered technology. The goal of the HPV Challenge is that someday a HPV will be designed that is practical enough for everyday uses such as going to the store or commuting to work. It is true that for years the bicycle has offered a relatively cheap and environmentally friendly alternative for commuters but it is hampered by some major drawbacks. First, the rider is exposed to the elements making use in harsh climates unappealing. Also, many conventional bicycles are limited in their top speeds due to wind resistance and driver strength. These two major drawbacks of the bicycle can be reduced by creating an aerodynamic cover called a fairing. This will reduce the drag coefficient on the bike and shelter the rider. As senior mechanical engineering students at Portland State University we have chosen to combine the ASME HPV Challenge with our senior Capstone project. 14

16 Explanation of This Document This Product Design Specification (PDS) defines the external and internal customers, the project requirements, design constraints, and the priority of those constraints. Conclusions are also drawn as to the decision making process, customer feedback, and the project goals. Requirements for this document set by ME 492 are listed in Appendix C along with the page on which they are addressed on. Identification of Customers The primary external customer for this project is the PSU HPV Race Team since they will be the end users of the HPV and depend on its performance to win the HPV Western Region Challenge. The primary internal customer is ME 492/493 Capstone Course, which sets many of the projects milestones and presentation requirements. The PSU HPV s faculty advisor is also an internal customer because he ensures the project is on time, on budget, and meets all Capstone requirements. The final internal customer is the PSU HPV team because the project is ultimately a reflection on them. Customer Feedback This project differs from other capstone projects in several ways. First is the accelerated timetable. This pushed design meetings and decisions to be made between September and December. Second the primary external customer consisted of the same group of people as the primary internal customer; this gave the design team less resources for design constraints or input. As a result the team relied heavily on team decision making and the rules of the ASME Western Region HPV Challenge in the design process. Feedback from internal customers comes from weekly design meetings with the PSU HPV team and its faculty advisor. In these weekly meetings design criteria was established, team goals were set, and design decisions were made. Product Design Specifications The product design specifications are listed in three tables below and grouped in descending order of importance. 15

17 Table 1A: High priority product design specifications Criteria Requirements Primary Measurement Metric Target Target Basis Verification Method Customer Performance Top speed PSU-HPV Team Top speed in male and mph >45 mph Competition Vehicle Time trial research female sprint races research Braking ASME HPVC Stopping distance at Feet =< 20ft Competition rules Vehicle testing Judges 15mph Strength ASME HPVC Frame safety factor Non-dimensional >1.5 Competition Design analysis Judges research Strength PSU-HPV Team Fairing strength Flexure modulus Greater than or Competition Materials testing equal to 2007 PSU HPV fairing research Crash recovery PSU-HPV Team Time to self-upright Seconds < 15s Competition Vehicle testing research Turning radius ASME HPVC Judges Turning ability Radius in feet < 25ft HPVC rules Vehicle testing High-speed stability PSU-HPV Team Vehicle does not wobble uncontrollably at straight line speeds > 20mph Straight line aerodynamic efficiency Partial fairing removal for rider entry and exit Documentation Fulfill ME 492/493 Class Requirements Life In Service HPV needs to last through construction, testing, and HPV Challenge. Steering axis rotation in degrees < 5deg Competition research PSU-HPV Team Coefficient of drag Non-dimensional <=.14 Frontal area is an improvement upon Vike Trike II fairing PSU-HPV Team Rider change out time Seconds <60s Improve upon Vike Trike II fairing PSU-HPV Team Score on capstone related reports Grade A ME 492/493 class syllabus PSU-HPV Team Life of bike Months > April 2008 Bike must last until HPV Challenge is over Vehicle testing Theoretical verification with CFD and achieved with wind tunnel testing Time trial testing Inspection of class grade Inspection 16

18 Table 2A: Medium priority product design specifications Criteria Requirements Primary Customer Aesthetics Visual appeal ASME HPVC Judges Measurement Metric Target Target Basis Verification Method Frame appearance and competition presentation Points, subject to judges interpretation 30 points Competition rules Review points awarded at competition Criteria Requirements Primary Measurement Metric Target Target Basis Verification Method Customer Performance Maintenance PSU-HPV Team Industry standard bike Common bike tool = 100% Competition research Vehicle Time trial research tools sizes, percent Maintenance PSU-HPV Team Ease of access # of parts to remove to get to desired part <= 1 part Direct comparison to standard recumbent Solid modeling, vehicle testing bikes Light weight PSU-HPV Team Vehicle assembly lbs < 50 lbs Improve upon Vike Measurement with scale Trike II fairing and frame Cost Stay under budget PSU-HPV Team Stay under budget with material and fabrication cost Dollars > Budget Competition research Expenditure accounting Safety Rider safety PSU-HPV Team Visibility Degrees of vertical and horizontal view Table 3A: Low priority product design specifications Horizontal > 150 degrees Vertical > 60 degrees Rider preference Fairing Strength Modulus of elasticity >= Vike Trike II Experience of previous fairings adequate strength Measurement Vehicle testing Criteria Requirements Primary Measurement Metric Target Target Basis Verification Method Customer Ergonomics Rider comfort PSU-HPV Team Comfortable Deg F > 65 deg Competition research Vehicle testing temperature Ventilation Energy out, Watts Energy out = Energy in Competition research Vehicle testing 17

19 House of Quality The House of Quality (see Table 4A, below) is used to numerically compare customer needs (design criteria) and requirements, with 5 meaning high importance and 0 meaning no importance. Direct competitors are given an overall score in each of the design criteria. Table 4A: House of Quality Customer Needs Performance Safety Cost Weight Ergonomics Aesthetics Target Verification Priority High High Medium Medium Low Low Engineering Parameters Speed mph Measurement Braking <20ft Measurement Frame Strength SF 1.5 Analysis Turning Radius <20ft Measurement High Speed Stability <5deg Analysis Low Speed Stability <25ft Measurement Crash Recovery sec Measurement Rider Change Time <=60sec Measurement Drag Coefficient <=.14 Analysis Riding Geometry Analysis Crash Safety Measurement HPV Mass <25lbs Analysis Competition Bacchetta Giro 20 TT Recumbent HP-Velotechnik Recumbent

20 Conclusion The ASME HPV Challenge provides a unique set of obstacles and rewards as a senior capstone project. This project differs from other capstone projects largely because it is a design competition which is not an industry partnership where a specific product is developed or problem solved. This provides the HPV design team freedom in determining solutions to design problems. The goal of this project is to win the ASME Western Region HPV Challenge and complete all course requirements for the PSU senior capstone course. A design is sought that maximizes top speed, efficiency, ergonomics, and maneuverability to field the most competitive HPV within the limitations of the team budget. 19

21 Appendix B: Frame Configuration The conceptual design required a decision on whether the vehicle would be configured as a bicycle or a tricycle. Each configuration has consequences for design criteria of performance and cost. The performance requirements of top speed, stability, weight reduction, crash recovery, and straight-line aerodynamic efficiency are effected by the design decision. Differences in amounts and types of materials used can affect the cost requirement of staying under budget. Bicycle and tricycle configurations were evaluated in a table of pros and cons, which can be seen in Table 1B below. Table 1B: List of pros and cons for bicycle and tricycle configurations. Bike Trike Pros Cons Pros Cons Less components means lower Low-speed instability Low-speed stability High-speed instability weight and cost Small frontal area Tolerancing (front and back Team has experience working on Scrub wheel linearity) tricycle HPVs Low weight Rider change out requires pit Uncomplicated chain routing Steering design and use crew assistance Statistically win Crash recovery is complicated in a fully enclosed fairing Rolling resistance is increased with third tire Drive train has to be routed to avoid the front tire Aerodynamic resistance is increased with hole in the fairing for the third wheel The cons to the tricycle configuration are inherent to the tricycle design. Cons to a bicycle configuration can be overcome with engineering. The pro of experience for the tricycle reason can also be used to help the team with building a bike. Pros to a bike are intrinsic to a bike setup and they would be difficult (or impossible) to transfer to a tricycle setup. Therefore, the decision was made to go with the bicycle configuration. After determining the overall configuration of the frame concepts were started. The Vike Trike II contained entities that worked very well for the overall style of the competition. Keeping in mind the frequent rider changes and body configuration angles for each rider an iteration of the Vike Trike II was used to base our design. Maintaining the same rider height relative to the 20

22 ground as the Vike Trike II was must for a low center of gravity for a bike configuration. Figure 1B, 2B, and 3B (Below) shows a view of the frame in its final design state. Figure 1B: Vike Bike I Isometric View Figure 2B: Vike Bike I Side View 21

23 Figure 3B: Vike Bike I Front View 22

24 Appendix C: Fairing Material Selection Summary Section: The Human Powered Vehicle s aerodynamic fairing is an important safety and performance aspect of the vehicle. The fairing needs to maintain structural integrity upon impact yet be light weight. Six composite material configurations were tested against the 2007 Portland State University Vike Trike II HPV fairing for flexure modulus (ksi) and deflection at yield (in) with a three point flexural test, and density (lb/ft^3) using length measurements and a mass scale. Five samples of each configuration were tested to obtain an average. The results from the three point flexure test are given in force (lbf) and deflection (in). Flexure modulus is then calculated from force and length measurements of the sample. Density was calculated from length (in), width (in), thickness (in), and mass (g) measurements. Results Table 1C: Average of the test results Configuration Density (lb/ft^3) Deflection at Yield (in) Flexure Modulus (ksi) A (Vike Trike II) B C D E F G Table 2C: Fairing material selection comparison Configuration Density (lb/ft^3) Deflection at Yield (in) Flexure Modulus (ksi) A (2007 Vike Trike II) E (2008 Vike Bike 1) Evaluation Configuration E was chosen for the Vike Bike 1 HPV because it is the only configuration that has a greater deflection at yield and flexure modulus, while having a density less than the Vike Trike II fairing, (see table 1C, and 2C, above). A greater deflection at yield was desired because it 23

25 allows for a larger amount of energy to be absorbed by the fairing during an impact before failing. The greater flexure modulus provides a stiffer and stronger fairing, the larger deflection at yield allows for a larger amount of energy to be absorbed by the fairing before failing, and the lower density reduces overall mass of the fairing. Formulation Section Given: Experimental data and graphs from (Lou, Patton, Chamberlain 2008) Table 3C: Fairing composite material combinations (Lou, Patton, Chamberlain 2008) Configuration Material Layers Orientation Core Layup Method Layers A (Vike Trike II fairing) S2 fiberglass 0-90 Baltek Mat Air 3 B S2 fiberglass 0-45 Baltek Mat Vacuum 3 C S2 fiberglass 0-90 Baltek Mat Vacuum 2 D S2 fiberglass 0-90 Baltek Mat Vacuum 3 E S2 fiberglass 0-90 Balsa (3/32) Vacuum 3 F S2 fiberglass 0-45 Balsa (3/32 ) Vacuum 3 G S2 fiberglass 0-45 Balsa (1/8 ) Vacuum 3 24

26 Bending Modulus (ksi) Bending Modulus (ksi) Sample A Sample B Sample C Sample D Sample E Sample F Sample G Density (lb/ft^3) Figure 1C: Flexure Modulus vs. Density (Lou, Patton, Chamberlain 2008) Deflection at Yield (in) Sample A Sample B Sample C Sample D Sample E Sample F Sample G Figure 2C: Flexure Modulus vs. Deflection at Yield (Lou, Patton, Chamberlain 2008) 25

27 Find: The material configuration that will have a flexure modulus and deflection at yield greater than and a density less than configuration A, the Vike Trike II fairing. Assumption: 1. Configuration A creates a comparison between the Vike Trike II and other configurations 2. Configuration B tests the effect of fiber orientation 3. Configuration C tests the effect of number fiber layers 4. Configuration D tests the effect of vacuum bagging 5. Configuration E tests the effect of balsa wood 6. Configuration F is the experimental hypothesis 7. Configuration G tests the effect of a larger balsa wood core Solution: Table 3D, above, describes the fiberglass used, fiber orientation, core material, layup method, and number of layers used in each configuration. Figure 1C, above, shows that the differences between densities of configurations A, B, C, and D are insignificant. This does not satisfy the requirement of have a density lower than the Vike Trike II HPV, thus configurations B, C, and D are not a suitable fairing material. Figure 2C above, shows that configuration G has a lower deflection at yield than configuration A while configuration F has is about equal. This leaves configuration E which has a greater deflection at yield and flexural modulus than configuration A, while having a lower density. Analysis references 1) American Society for Testing and Materials Annual Book of ASTM Standards. Designation D Standard Test Methods for Flexural Properties of Unreinforced and Reinforced Plastics and Electrical Insulating Materials: ) Lou, Kenneth. Patton, Levi. Chamberlain, Erik ME 411 Final Experiment. Analysis of Fiber Reinforced Plastics for the ASME Human Powered Vehicle Fairing:

28 Appendix D: Drive Train Configuration The PSU Vike Bike I drive train configuration follows that of the conventional upright bicycle drive train. This helps keep the drive train cost down using industry standard components. The difference in performance criteria between front wheel drive and wheel drive and rather close but drive train begins to get complicated very fast when dealing with front wheel drive. Top speed listed in the PDS as a large performance criteria for the Vike Bike I and as a result forced the gearing selection to be non industry standard. A 75 tooth and 65 tooth chain rings were manufactured for top speed achievement and easy adaptability to industry standard components. Table 1D (below) is a list of pro s and con s for the Vike Bike I drive train. Table 1D: Drive Train Configuration Pro s and Con s FWD RWD Pro s Con s Pro s Con s Small chain line, high efficiency Limited wheel size and gearing constraints Ability to use large wheel while keeping center of gravity low Long chain line, low efficiency Easy chain routing Chain twisting will cause pre-mature ware of chain. Conventional configurations and proper use of parts Complicated chain routing to rear wheel Complicated configuration provides expensive parts Use of commercially available parts Examples of each drive train are shown below in figure 1D, and 2D Figure 1D: Low racer Front wheel drive train configuration 27

29 Figure 2D: Vike Bike I concept Rear wheel drive train configuration 28

30 Appendix E: Turning Analysis Summary Section ASME rules state that a vehicle must be able to turn within a 25ft radius. A geometric analysis was performed to see how many degrees the fork of Vike Bike I must turn to fit within this circle. Through solid modeling, it was found that the maximum amount that the steering tube could rotate was degrees. Since the steering tube and fork are connected directly, this is also the maximum amount that the fork is able to turn. With this information, the minimum achievable turn radius (in feet) was calculated. The results of the analysis listed below: a) Turning angle required to achieve 25ft turn radius 10.6 deg b) Turning radius with a degree turning angle 8.7 ft Each situation was modeled for worst-case scenario. After starting the initial turn, the angle required to continue the turn will decrease. Leaning into the turn also decreases the turning angle required. Taking continuing a turn and leaning into account, the amount of turning angle and the turning radius will decrease. Therefore, the design meets and exceeds ASME standards. Formulation Section Given: Figure 1E (below) shows Vike Bike I having a wheelbase of inches. The maximum angle that the steer tube can turn without hitting the fairing is degrees, as shown in Figure 2E below. 29

31 Figure 1E: Top view of the Vike Bike. The wheelbase measurement is important in the view plane (i.e. Delta X) only. Figure 2E: When the steer tube has reached its maximum swing, the angle between the steer tube and the main tube is deg, measured from the top view. Find: a) The angle that the fork must turn to achieve the ASME required turn radius of at least 25ft. b) The turn radius when the steer tube is at degrees. Assumption: 8. Leaning when riding improves the turn radius, and not leaning corresponds to lower speed biking. Performing the analysis without taking leaning into effect will be considered as a worst case scenario. 9. Starting the turn requires more of a turning angle than continuing the turn. Therefore, only the initial angle will be considered as a worst case scenario. Solution: a) 30

32 A sketch of the system at the start of a low speed turn is provided in figure 3E, below. Figure 3F: Sketch of the wheelbase (solid line) and the 25 foot circle with radius (dashed line). All dimensions are in inches. The front wheel is coincident with the curve (see figure 3E, above). To turn the Vike Bike in the circle, the front wheel must be turned at an angle from the frame until it is tangent with the circle. A right triangle is created from figure 3F and is shown in figure 4E, below. Figure 4E: Sketch of tangent line (solid line) and right triangle. Hyp is the hypotenuse and the radius of the circle, b is the wheelbase, and a is the desired angle. By geometric association, it can be seen that the desired angle is the same an angle in the right triangle (see figure 4E). Angle a is found using equation 1F a asin b hyp (Eq. 1F) Substituting values for b and hyp into equation 1E yields the desired angle. a asin a 10.6deg 31

33 Desired angle for the ASME prescribed minimum turn radius of 25ft. b) A sketch of the system with the given information is provided in figure 5E. Figure 5E: Sketch of the wheelbase and turn circle when the fork is turned to Solving equation 1E for the hypotenuse gives: its maximum angle. hyp b sin( a) (Eq. 2F) Substituting the values of a and b into equation 2F yields: hyp 54.95in sin( 31.88) hyp in Converting the turn radius to feet yields: hyp 8.7ft For the turn radius when the steering tube is at an angle of degrees. 32

34 Appendix F: Fairing configuration The most important job of the fairing is to reduce the drag force exhibited on the bike so for a given power output by a rider the bike will have a higher velocity. Each of the configurations below address this issue to varying degrees. Beyond the reduction of drag forces there are other facets of the fairing design that must be considered. Manufacturing time and cost are budgetary constraints, while rider ergonomics must always be kept in mind to maximize power output and safety. A list of pros and cons of each configuration is given in the table below. Table 1F: A comparison of three possible fairing configurations Symmetrical Fairing Non-Symmetrical Fairing Partial Fairing Pros Cons Pros Cons Pros Cons Moderate manufacturing cost High weight when compared to the partial fairing Best reduction of drag force High manufacturing cost No manufacturing cost Low reduction of drag force Moderate manufacturing time Reduction in drag force is nearly as good as the nonsymmetrical fairing Poor crash recovery High manufacturing time No manufacturing time High materials cost High materials cost Low materials cost Good visibility must be High weight when Low weight designed compared to the partial fairing Ventilation must be designed Poor crash recovery Good visibility must be designed Ventilation must be designed Best crash recovery Good rider visibility is inherent Good rider ventilation is inherent Though the partial fairing has the most pros, they do not compensate for its deficiency in drag force reduction. The non-symmetrical fairing has the highest reduction in drag force but the time and cost associated with such a design is prohibitive. Given the time and budget constraints the symmetrical fairing is chosen for its high reduction in drag force. The symmetrical design reduces manufacturing time and cost by requiring fewer positive and negative molds to produced. Only a single negative mold is needed to produce both the top and bottom half of the fairing since the intended shapes are identical. Keeping this manufacturing process in mind the shape of the fairing can be designed conforming to the requirements outlined in the PDS. The set of requirements for the fairing are as follows: - Reduced drag force when compared to previous PSU fairings - Complete coverage of the bike frame and rider (full fairing) - Accommodations for rider ergonomics 33

35 Choosing the planar shape was the first step in the design. The 2006 HPV team used a shape provided by the National Advisory Committee for Aeronautics (NACA). The shape was chosen for its pressure recovery attributes as well as fitting the geometry of the 2006 trike. Selection of the planar geometry for the 2008 bike was done by using a 6-series NACA shape that would contribute to a reduced drag force while closely fitting the shape of the 2008 Bike. Table 2F: A comparison of the Planar shapes for the 2006 and 2008 HPV fairings PSU 2006 Planar Shape PSU 2008 Planar Shape Pros Cons Pros Cons Good pressure recovery Frontal area is larger than necessary for the 2008 bike Better pressure recovery due to increased laminar flow Space for pedals and feet will be reduced. Plenty of room for pedals and feet Smaller frontal area One of the reasons increased pressure recovery is expected of the 2008 fairing is because its maximum width occurs further from its leading edge. This is readily apparent when comparing figure 1F and figure 2F. Note that both fairings have a nose to tail length of 106. Figure 1F: PSU 2006 Planar shape Figure 2F: PSU 2008 planar view A NACA 4-series shape determines the leading 2ft of the fairing, after that the geometry is governed by rider dimensions, the rollbar and toe box (the toe box is highlighted in figures 1F 34

36 and 2F). The non-symmetrical geometry of the bike frame requires that the fairing is not symmetrical top to bottom. The modification to the symmetrical design can be seen in figure 4. The result is that the bottom of the fairing is flat while the top is curved. Figure 3F: PSU 2008 side view Achieving the flat bottom requires minor changes to the manufacturing process. Once the top of the fairing is constructed, the mold will be modified by inserting a restrictor plate that changes the inner dimensions of the mold. The plate is made of ¾ plywood that is painted and waxed so the surface matches that of the mold. The plate, mold and inserted plate location can be seen in figure 4F. This simple modification requires little manufacturing time and cost and retains the benefits of a single negative mold system. Restrictor Plate Restrictor Plate location Figure 4F: View of mold and plate 35

37 The final design completely encloses the rider and the bike, allows adequate room for the toe box and is expected to have a reduced drag force when compared to previous PSU HPV fairings. 36

38 Appendix G: Straight line aerodynamic efficiency Summary Section The goal is to verify that the drag forces have been reduced when compared to the Vike trike 06/07 fairing. By manipulation of the shape of the fairing, specifically in the planar view as shown in figure 1I, the coefficient of drag and the frontal area will be reduced when compared to the Vike Trike II. Frontal Area= 864 in 2 To date the frontal area of the 2008 fairing has been verified as being smaller than previous years. This was found using Solid modeling. Formulation Section Given: Solid model of the Vike Bike s external surface below. Figure 1G: Planar view of the Vike Bike fairing Find: a) The frontal area b) The coefficient of drag (to date this has not yet been completed) Assumptions: -External flow is normal to the frontal area of the fairing. -The fairing is completely sealed with no ventilation or wheel cutouts. Solution: 37

39 -The frontal area of the 06/07 fairing is found using the SolidWorks tool Section Properties. The frontal areas of the fairings can be seen in the figures below. 886in 2 864in 2 Figure 2G: 2006/07 Fairing frontal area Figure 3G: 2008 Fairing frontal area The 2008 faring has a frontal area of 864in 2 while the 2006/07 fairing has a larger surface area of 886in 2. This gives a 2.5% reduction in frontal area. 38

40 Appendix H: Finite Elemental Analysis Summary Section Finite elemental analysis (FEA) was performed with I-DEAS 5 to analyze stress, strain, displacement, modal frequency, and weight in the Vike Bike I frame. An optimization procedure was used to find commercially available tube sizes that would give the highest stiffness and lowest weight while making sure to stay above the required safety factor of 1.5. The Vike Bike I was modeled to show compliance with ASME rollbar standards that say the frame shall not yield or fracture in a top loading of 485lbf or a side loading of 260lbf. A materials selection analysis helped determine that Aluminum 6061 would be used. The final optimization results are presented in Table 1H (below) for stress (psi), factor of safety against material failure and yielding. Table 2H (below) shows the final optimization results for modal frequency (Hz) and weight (lbf). Table 1H: Stresses and factors of safety in different loading conditions Final Optimization Maximum Von Mises stress (psi) Yield strength (psi) Factor of safety against yield Top Load Side Load Frame Side Load Fork Fatigue Factor of saftey (ASME/Gerber) Main tube Boom / /1.7 Table 2H: Frame modal frequencies and weight Final Mode 1 (Hz) 20 Mode 2 (Hz) 46 Mode 3 (Hz) 62 Mode 4 (Hz) 72 Mode 5 (Hz) 100 Frame Volume (in^3) Frame Weight (lbf) Optimization

41 Formulation Section Given: Model of the Vike Bike I and II, reported by 2007 PSU HPV Team in their ASME Design report, show rider weight of 100lbf at the seat tube bends, 1680in*lbf moment about the z axis, and a 1320 lbf moment about the y axis (see Figure 1H, below). Vike Trike I and II displacement results are listed in Figure 2H. The ASME Interpretation of Rollover/side Protection Rules for 2008 HPVC Competitions states a top load of 485 lbf and a side load of 260 lbf (see Figure 3H), where the loads are applied independently. Figure 1H: FEM with Boundary Conditions for the Vike Trike II. Table 3H: Comparison of Stress and Displacement for Vike Trikes I and II. 40

42 Figure 2H: Loading requirements determined by ASME Find: a) Model 2008 Vike Bike design and determine the maximum stress and displacement using 6061 Aluminum. Show validity of model through convergence. Compare results to Vike Trike II. b) Find maximum stress and displacement using the same model as in part (a), using Titanium and 4140 steel. Compare results. c) Perform a modal analysis of the three models in part (b). Compare results. d) Select frame material. e) Using ASME top and side loads, show that the roll bar is acceptable and that there is no permanent deformation or fracture on either the roll bar or the vehicle frame. Find factor of safety against fatigue failure. Assumptions: The fork, frame, and boom are all one piece. Dropouts, wheels, headset, cranks, and bottom bracket are not modeled because they are design to withstand bicycle loading. 41

43 ASME top and side loads are not considered cyclical and are not used in a fatigue analysis. Rider weight is a point load in the seat tube bends. Solution: a) Geometry The geometry was created with as a 3-D wireframe sketch in Solid Works and imported into I- deas 5. Beam cross sections were keyed in for the seat tubes, roll bar, head bar, boom, main tube, forks, and fork bends. Where the tube and main tube come together and where the head tube and steer tube come together were both modeled as beams with the outer diameters of the bigger beam and the inner diameter of the smaller beams. Mesh- Meshes were created using the beam mesh option in I-deas. Four meshes using 6061 Aluminum for the body and generic isotropic steel were created. Different element sizes were used to show the solutions convergence. Meshes 1 through 4 had 113, 161, 257, and 283 elements respectively Boundary Conditions - To compare stress and displacement to Vike Trike II, similar loading and restraints were employed to those shown in figure 1, above. Two point loads of 100lbs each were applied to the seat tube bends. The rear dropouts were fixed from translation, and the front dropouts were fixed from translation in the y and z axis. A boundary conditions set was then created. This was all accomplished under the Boundary Conditions task-icon, heat transfer mode. All of the constraints and forces included in the boundary conditions set can be seen in Figure 2 42

44 Figure 3H: Vike Bike I frame and boundary conditions for dynamic loading. Results - A solution set was created for the models with their boundary condition sets, and the models were solved under the Model Solution task-icon. Table 5H, below, shows the results for maximum Von Mises stress, x displacement, y displacement, z displacement, and strain energy for each of the meshes. The stress and displacement results converged almost immediately. The 283 element mesh was optimized to reduce the strain energy encountered from the 257 element mesh. Table 4H: Maximum Von Mises stress, displacement, and strain energy for each model. Elements Maximum Von Mises Stress (psi) X (in) Y (in) Z (in) Strain Energy (in*lbf) E E E E E E E E E E E E E E E E E E E E-01 43

45 2.50E+04 Maximum Von Mises Stress (psi) 2.00E E E+04 Maximum Von Mises Stress (psi) 5.00E E Figure 4H: Convergence of Von Mises Stress 1.60E E E E E E-02 X (in) Y (in) Z (in) 4.00E E E Figure 5H: Convergence of Displacement 44

46 4.50E+00 Strain Energy (in*lbf) 4.00E E E E E E+00 Strain Energy (in*lbf) 1.00E E E Figure 6H: Convergence of Strain Energy b) Mesh- Meshes were created using the 283 element beam mesh used in part (a). Meshes 1 through 3 were made with 4140 steel, 6061 aluminum, and typical titanium bodies, while maintaining the fork as generic isotropic steels. Tube sizes were kept the same for each mesh. Boundary Conditions - Boundary conditions were the same as in part (a). Results - A solution set was created for the models with their boundary condition sets, and the models were solved under the Model Solution task-icon. Table 4 (below) shows the results for maximum Von Mises stress, x displacement, y displacement, z displacement, and strain energy for each of the meshes. The Vike Trike II stress and displacement results are reproduced for ease of comparison. Titanium versus aluminum evaluation is included as well and shows a titanium displacement of 80% that of Aluminum. 45

47 Table 5H: Tabulated results of stress and displacement in each body Steel Al 6061 Titanium (Typical) Vike Trike II Ti vs Al (%) Maximum Von Mises Stress (psi) 2.34E E E E Max. Disp. X (in) 5.50E E E E Max. Disp. Y (in) 4.32E E E E Max. Disp. Z (in) 7.50E E E E Displacement Magnitude (in) 8.45E E E E Strain Energy (in*lbf) 6.67E E E+00 Figure 7H: Maximum Von Mises Stresses for 4140 steel, 6061 aluminum, and typical titanium 46

48 Figure 8H: Maximum Displacement for 4140 steel, 6061 aluminum, and typical titanium c) Mesh- Meshes were the same as the meshes used in part (b) Boundary Conditions - Restraints were the same as those used in parts (a) and (b). Boundary condition sets were made under normal linear dynamics, Lanzcos method. Results - A solution set was created for the models with their boundary condition sets, and the models were solved under the Model Solution task-icon. Below are the tabulated results for the first five modes in each model. The bike weight is included for each type of material. It can be seen that 4140 is too heavy to be used effectively 47

49 in the human powered vehicle. Aluminum 6061 provides the lightest bike weight by far, with similar modes to those found in 4140 and Titanium. Titanium offers 80% of the total deflection than that of Aluminum with similar tube sizes. Table 6H: Lanzco s method Modal analysis 4140 Steel Al 6061 Titanium (Typical) Mode 1 (Hz) 9.85E E E+01 Mode 2 (Hz) 3.13E E E+01 Mode 3 (Hz) 3.85E E E+01 Mode 4 (Hz) 7.39E E E+01 Mode 5 (Hz) 8.18E E E+01 Total Weight (lbf) Densities from efunda d) An aluminum frame with the same tube sizes is 56-60% the weight of a titanium frame, and 35% of the weight of the steel frame. Comparison of the Vike Bike (using aluminum) and the Vike Trike II shows the Bike with 56% of the total displacement than that of the Vike Trike. The Bike has 50% more stress which lowers the factor of safety from 4.46 to With the light weight of aluminum, adequate factor of safety, low cost, and ease of manufacture, it is recommended that Aluminum 6061 be used for the Vike Bike I frame. Table 8H (below) shows a comparison of the Vike Bike against the Vike Trike II. Table 7H: Comparison of Vike Bike and Vike Trike II Al 6061 Bike Vike Trike II Al. Bike vs. Trike (%) Maximum Von Mises Stress (psi) 1.21E E Max. Disp. X (in) 8.12E E Max. Disp. Y (in) 9.31E E Max. Disp. Z (in) 1.40E E Displacement Magnitude (in) 1.53E E Factory of Safety 3.06E E

50 e) Geometry The geometry was changed slightly to accommodate ease of manufacturing and new fork models. Mesh - Meshes were kept 283 +/- 20 elements. Boundary Conditions - For fatigue, the dynamic loading listed above was broken into mean and alternating loading conditions. A top loading and a side loading was created as per ASME rollbar standards. ASME guidelines specify that the fork and dropouts must be free from translation. This restraint set was used for all models. A modal boundary condition set was created using Lanzco s method. Results A sample (Final Optimization) calculation for fatigue in the Boom is provided: Fatigue analysis - Boom *All tables and equations refer to Mechanical Engineering Design, 7th ed., by Shigley S ut 38 ksi Ultimate strength in 6061-T6 aluminium S y 35ksi Yield strength in 6061-T6 aluminum S eprime 0.504S ut Endurance strength in 6061-T6 aluminium Marin Factors a 2.70 Machined parameters from table

51 b k a b as ut k a 1.03 d 1.75in 0.370d d e in Equation 7-18 Surface factor ka Boom diameter Equivalent diameter, equation k b 0.879d e k b Equation 7-19, for diameter.11<=d<=2in Size factor kb k c 1 k d 1 k e Loading factor for bending, equation 7-25 Temperature factor at 20 deg C, table 7-6 and equation % reliability factor from Table 7-7 S e k a k b k c k d k e S eprime Equation 7-17 S e ksi S e ksi Modified endurance factor m 9.79ksi a 7.65ksi a m Load line n y S y a m n y Factor of safety against first cycle failure 50

52 1 n f 2 a S e n f m S y ASME-Elliptic Failure Criteria, Table 7-11 Factor of safety against fatigue failure 1 n f 2 S ut ksi m 2 a 1 1 S e 2 m S e S ut a ksi Gerber Failure Criteria, Table 7-10 n f 1.67 Factor of safety against fatigue failure Fatigue in the main tube was analyzed with a similar method but with slightly different Marin factors to due to the different tube sizes. The results for each optimization, including the original and modified geometry, are included below. Table 9H shows the maximum stresses and factors of safety for the specified loading conditions. Table 10H shows the modal frequencies and weight for each optimization model. Table 8H: Maximum stresses and factors of safety for specified loading conditions First Approximation Top Load - Side load - frame Side load - Dynamic - Dynamic - fork frame fork frame Maximum Von Mises stress (psi) 4.42E E E E+04 Yield strength (psi) 3.50E E E E+04 Factor of safety against yield Optimization 1 Maximum Von Mises stress (psi) 4.43E E E E E+04 Yield strength (psi) 3.50E E E E E+05 Factor of safety against yield Optimization 2 Maximum Von Mises stress (psi) 6.18E E E E E+04 Yield strength (psi) 3.50E E E E E+05 Factor of safety against yield

53 Top Load - frame Side load - frame Side load - fork Dynamic - frame Dynamic - fork Optimization 3 Maximum Von Mises stress (psi) 5.63E E E E+04 Yield strength (psi) 3.50E E E E+04 Factor of safety against yield Optimization 4 Maximum Von Mises stress (psi) 1.05E E E+04 Fatigue Factor of saftey Yield strength (psi) 3.50E E E+05 Main tube boom Factor of safety against yield / /3.2 Optimization 5 Maximum Von Mises stress (psi) 5.36E E E+04 Fatigue Factor of saftey Yield strength (psi) 3.50E E E+05 Main tube boom Factor of safety against yield / /3.3 Optimization 6 Maximum Von Mises stress (psi) 5.35E E E+04 Fatigue Factor of saftey Yield strength (psi) 3.50E E E+05 Main tube boom Factor of safety against yield / /3.3 Optimization 7 Maximum Von Mises stress (psi) 7.32E E E+04 Fatigue Factor of saftey Yield strength (psi) 3.50E E E+04 Main tube boom Factor of safety against yield / /2.4 Final Optimization Maximum Von Mises stress (psi) Fatigue Factor of saftey (ASME/Gerber) Yield strength (psi) Main tube Boom Factor of safety against yield / /1.7 Table 9H: Modes and weight for each model Origin al Optimizatio n 1 Optimizati on 2 Optimizati on 3 Optimizati on 4 New Geometry Optimizati on 6 Optimizati on 7 Final Optimizati on Mode 1 (Hz) Mode 2 (Hz) Mode 3 (Hz) Mode 4 (Hz) Mode 5 (Hz) Frame Volume (in^3) Frame Weight (lbf)

54 Analysis references: Shigley, J.E Mechanical Engineering Design. 7 th ed. New York: Mcraw-Hill American Society of Mechanical Engineers Interpretation of Rollover/side Protection Rules for 2008 HPVC Competitions. HPV/13615.pdf (10 March 2008). 53

55 Appendix I: Biomechanical Testing Summary Section For the finite element model of the frame it is important to apply accurate forces insuring that the frame is not overbuilt this helps cut the overall weight of the Vike Bike I. A top speed analysis will also be more accurate knowing the actual forces and power the riders are able to subject the bike to. These forces are measured in the x, y, and z directions using a PCP Piezoelectric force transducer model U206A203 that is attached to the Vike Trike II pedal as seen in figure 1I. A Model Shop low speed laser tachometer was also used to measure the cadence for each rider. Figure 1I: PCB Force Transducer bicycle pedal adapter The testing was performed on the Vike Trike II with the use of LABView and a NI-9233 data acquisition device. The PDS states that the Vike Bike I will reach a top speed greater than 45 miles per hour. With this testing the Vike Bike I s top speed can me more accurately calculated. The PDS also lists a light overall weight of the Vike Bike I. The biomechanical testing will help the design team design the frame so that it is light and strong enough to withstand the loading each rider will produce while riding. The PCB force transducer s output signal is a voltage in each direction x, y, and z. A conversion factor is determined through testing and calibration from PCB allowing the conversion from mv to Newton or pound force. The signal output for the laser tachometer is also voltage that can be tabulated using the virtuial instrument. The data can then be graphed comparing the resultant force for x, y, and z to the rider cadence. Below a table was constructed showing the rider maximum force and cadence. 54

56 Table 1I: Rider force output, cadence Rider Max Force (Lbf) Average Force (Lbf) Cadence (rpm) Max Power (Hp) Average Power (Hp) Ben Bryan Chantelle Erik Kenneth levi Formulation Section Given: Figure 2I Figure 2I: Rider resultant force and cadence output for 5 seconds. Find: -Moments about center of bottom bracket. Assumptions: -Ignore losses in pedal connection and bottom bracket. Solution: Force 104.5lbf crank_radius 175mm M bb Force 2crank_radius M bb ftlbf Analysis Reference: Bolen, Ben and Bryan Voytilla ME 411 Final Lab Report 55

57 Appendix J: Vehicle Stability Recumbent bicycle stability is dependent on the wheel base and tail a bike or trike has. A large trail, more than 3.5 and long wheelbase in excesses of 60 leads to better high speed stability. While a short wheel base of less than 60 and a smaller trail less than 3.5 allows for better handling at low speeds. Head tube angle in relation to the ground also known as steering axis angle, can help improve high speed stability. Conventional upright bicycles are anywhere from Figure 1J (below) and also apply to human powered vehicles. Figure 1J shows a diagram of the Vike Trike II front wheel configurations. With the value of trail of 2 1/8 the Vike Trike II was found to be very twitchy for high-speed stability. Figure 1J: Vike Bike head tube angle design configuration Figure 2J: Vike Trike II Front wheel configuration 56