Hpvc Capstone Final Report

8/10/2019 Hpvc Capstone Final Report

1/21

5711 BOARDMAN HALL

DEPARTMENT OF ORONO, ME 04469-5711

MECHANICAL ENGINEERING TEL: 207 581-

2120 FAX: 207 581-2379

ASME Human Powered Vehicle ChallengeCapstone Group

End of Semester Report


2/21

1

Table of Contents

Introduction ............................................................................................................................................... 2

The Design Process ................................................................................................................................... 2

Factors that Impact Design ....................................................................................................................... 3

Initial Design Choices............................................................................................................................... 4

Pre-design Calculations ............................................................................................................................ 4Design Choices ......................................................................................................................................... 6

Second Design Iteration ............................................................................................................................ 7

Competition Venue ................................................................................................................................... 8

Recumbent Testing ................................................................................................................................... 9

Third Design Iteration............................................................................................................................... 9

Computational Fluid Dynamics .............................................................................................................. 10

CFD Verification .................................................................................................................................... 11

Verification Methods .............................................................................................................................. 11

Verification with Temples HPV Fairing Design ................................................................................... 12

Fairing Iterations and CFD Analysis ...................................................................................................... 12

Fairing and Frame Integration ................................................................................................................ 14

Moving Forward ..................................................................................................................................... 14


3/21

2

Introduction

This capstone project is aimed at designing and building a human powered vehicle to compete in the

ASME Human Powered Vehicle Challenge. From the ASME HPVC rule book, the objective for thiscompetition is:

To provide an opportunity for engineering students to demonstrate application of sound engineering

principles toward the development of fast, efficient, sustainable, and practical human-powered vehicles.

During the competition, the team will be scored on the design of the human powered vehicle, innovation in

the area of human-powered transport, reliability of performance, speed, and practicality of the overall

design.

As part of this challenge, we need to be able to develop a vehicle capable of coping with the everyday tasks

that any other fossil-fuel-powered vehicle would encounter. We have to design a vehicle that is capable of:o Coming to a complete stop while maintaining complete stability of the vehicle.

o Accommodating small parcels.

o Clearing road debris/obstacles such as a speed bump, rocks, or branches.

o Turning within a 25 foot radius and completing a pre-determined obstacle course.

o Completing all tasks listed above while maintaining driver safety and vehicle control.

Our group has decided to make a faired recumbent vehicle to compete in the ASME competition. Since thiswill be the universitys first HPV team in over 7 years, we have decided to concentrate our vehicle design

toward the speed and endurance events of the competition. We may be a small, new team to thecompetition, but by focusing on these two aspects, we hope to ensure that an individual event title is within

our grasp.

The Design Process


4/21

3

Factors that Impact Design

In order to identify the best solution for the problem at hand, we first had to complete some research on the

workings of conventional and recumbent bicycles. The biggest influences for the design of our fairedrecumbent bicycle were bicycle dynamics and aerodynamics. The aerodynamic portion of the bicycle wasthe first influence that was considered for our design, and helped to constrain the variables that affected the

overall layout of our human powered vehicle.

Without knowing the details of the frame, only conceptual aerodynamics of the vehicle were considered.Any aerodynamic drag enacted on the vehicle is due solely to the coefficient of drag and the frontal area of

the vehicle. The coefficient of drag is a product of the fairing shape, which can be thought of as

independent of frame design. Considering frontal area plays a large role in bike design. Frontal area is acoupled issue where frame design will directly affect the drag forces seen by the vehicle. A bike design is

begun with the primary constraint being minimizing frontal area. In an attempt to reduce frontal area, a

two-wheeled recumbent bike was chosen. Two wheels allows for the bike to be significantly narrower thanan equivalent design with more wheels. Additionally, the choice of a recumbent bike allowed for an overallvehicle height ranging from 6-28 inches shorter than a conventional diamond-frame bicycle.

When starting our research, no one on the team had any previous experience with recumbent bicycles. We

were all familiar with the way diamond-frame bicycles react to various rider inputs, but the dynamics ofrecumbent bicycles were unknown to us. The four critical characteristics that affect bicycle dynamics are

shown below in Figure 1:


5/21

4

These components combine to create an unstable system, which is only stabilized by adding a human rider.Whether we know it or not whenever we ride a bike we are performing many complex micro adjustments

to the bike as we move. These adjustments are actions such as rotating the handlebars a small amount, or

shifting our weight a little to one side, forward, or backward. Considering all of these effects with the factthat recumbent bicycles are lower to the ground, with a lower center of gravity, culminates in the fact thatrecumbents are less stable then their upright cousins. Because of this, it is especially important to consider

the factors presented above such as rake, head angle, and wheelbase when designing our humans poweredvehicle.

Initial Design Choices

Once we had completed enough research to begin designing our human powered vehicle, we made a fewcritical design choices that would influence the rest of our recumbent vehicle. In order to finish near the topof the ranks in the endurance and speed events in the competition, we decided that having a high top speedwould be an important characteristic in our vehicle. As such, our first design choice was to make the

vehicle capable of reaching 55mph under only human power, without the assistance of a downhill slope or

a tailwind. This design choice influenced many of the successive design choices due to the fact that not all

choices would allow for such a speed to be reached.

In order to achieve these high speeds, a very aerodynamic vehicle would be needed. In order to decreasethe overall height of the bike, it was decided that we would use 20 inch wheels. This reduction in height

would significantly reduce the projected area of the vehicle, and as a result, the resistive drag forces wouldbe decreased.

Once the decision had been made to reach such high speeds, we had to determine how to stop the vehicle

safely and effectively. Stopping a recumbent bike poses many stability issues. The competition states thatall vehicles must be able to start and stop without assistance. A fully faired, two-wheeled recumbent cant

do this without tipping over. Accordingly, we decided that a stability system would be required. To includea stability system without affecting the aerodynamic characteristics of the vehicle it was determined that the


6/21

5

Figure 2 Required gear ratio vs. drive wheel diameter for various top speeds.

For a 20 inch drive wheel, it was found that a mechanical advantage of 7.70:1 would be required to reach a

maximum speed of 55 mph. On diamond-frame race bikes with front and rear derailleurs, the maximumgear ratio is around 5:1. Accordingly, in order to reach our desired speed, we would have to forgo having a

front derailleur on our vehicle, and use a single, large chainwheel. With such a system, a minimum gearratio of 2.5:1 is required, while most conventional road bikes have a minimum gear ratio of 1.33:1.

Al h h l h i h l ld d h d bl i d h hi ld

0.00

2.00

4.00

6.00

8.00

10.00

12.00

16 20 24 26 27 28 29

Mechanica

lAdvantage

Tire Diameter (in)

Required Mechanical Advantage vs. Tire Diameter

Mech. Adv. 45

Mech. Adv. 50

Mech. Adv. 55

Mech. Adv. 60

Mech. Adv. 65


7/21

6

In our research on recumbent bicycles, we found multiple equations governing the drag force seen by afaired recumbent bicycle. Many factors such as the wind speed, the rolling resistance of the tires, the

drivetrain efficiency, and the ground speed of the vehicle affect the amount of drag, and further, the top

speed of the vehicle. Using an approximate projected area determined from other faired recumbentvehicles, it was determined that for a ground speed of 55mph, with a head wind of 10mph, a vehicle with adrivetrain efficiency of 0.85 would require an input force of 140lbf and a power input of about 1000 watts.

This amount of power is within the physical capabilities of an average human, and as such, helped validatethat our top speed could be achieved. Additionally, through further drag calculations, it was found that at

45mph, a faired recumbent bicycle sees the same drag force as a conventional diamond-frame bike

travelling at 15mph a 30mph difference! Tabular aerodynamic and gearing calculations are found inAppendix A of this document. With these calculations favoring our initial design choices, we started to

design our recumbent bike.

Design Choices

Based on our research on bicycles, recumbent bicycles, and human powered vehicles, our team began

completing the rest of the design choices required to fully define our vehicle. To determine the frame

layout, we had to determine the wheelbase length, driver position, steering type, adjustability options, etc.

which would allow us to build the vehicle we had envisioned. A complete list of our design choices isshown below in Figure 3.

Items Possible Design Options Design Choices

Driver Orientation Forward Facing, Recumbent Recumbent

Drive Type Front Drive, Rear Drive Rear Drive

Drive Wheel Size 29, 27, 26, 24, 20 20

Coaster Wheel Size 29, 27, 26, 24, 20 20

Top Speed 45-65 55 @ 110rpm

Steering Type Front Steer, Rear Steer FrontSteering location Driver Front, Under Seat, Center Driver Front

Fairing Access Removable sections, "doors" Removable Sections

Storage Location Front, Behind Driver, Under Driver Behind Driver Back (Behind Driver Head)

St bilit Aid F t D l bl Wh l M h l Th h l d hi l 2 D l bl h l


8/21

7

Overall, we decided to build a short wheelbase, recumbent mid-racer. It would have a 27 inch drive wheeland a 20 inch steering wheel. It would have driver-front steering and two deployable, lever actuated wheels

for slow-speed stability of the vehicle. It will feature a fiberglass fairing with a steel roll bar and a 3 point

harness if a rollover should occur during competition. Additionally, a compound geartrain would be usedwith the pedals located in front of the steering wheel.

Second Design Iteration

Now that our design choices had been solidified, it was time to begin our second frame and geartrain

iteration. To start, a detailed drawing of the frame was made by hand. The frame was sized to fit a 20 inchfront wheel and a 700C rear wheel with a 10-speed cassette. Based on these critical dimensions, the rest of

the frame was dimensioned around the driver, allowing for proper rider ergonomics while maintaining ourchosen short-wheelbase design. Once the entire frame had been dimensioned, stress calculations wereperformed along the length of the frame to determine the required wall thickness. It was determined that forthe main sections of our frame, a wall thickness of .089 inches was required. With this in mind all of the

dimensions for the frame were passed along for CAD modeling.

While the CAD modeling was being completed, we began designing the gear train that would allow us toreach the desired 55mph top speed of the bike. In order to give us a wide range of gear ratios, allowing for

top speed riding and starting from a stop on a hill, a compound gear train was required. A conventional3x10 gearing system was desired for our project, but due to the required 5.71:1 gear ratio, the gearing

system would need to be modified to allow for the higher gear ratio.

To increase the gear ration from the available 4.18:1 to the required 5.71:1, two pass-through locationswere added to the frame, with an increase in gear ratio at each location. Using shaft mounted sprockets, the

power generated at the cranks was passed along the frame until reaching the rear drive wheel. By allowingthe power to be transferred across the frame, we were able to balance the bending stresses along the left and

right sides of the frame, reducing the stress concentrations at each of the pass-through locations. Once thegeartrain had been designed, the rest of the frame sizing calculations were completed, and material was


9/21

8

After the frame had been fully modeled in SolidWorks, finite element analysis (FEA) was performed on theframe to determine the locations of maximum stress and the factor of safety of the frame. To construct the

frame, we planned to use square and rectangular steel tubing with a wall thickness of 0.089 inches.

According to the FEA results, for 1020 steel with a wall thickness of 0.089 inches, the minimum factor ofsafety of the was approximately 10. As such, the strength of our frame was more than adequate. Although ahigh factor of safety is beneficial in terms of reliability, it represents and overdesigned frame and excessive

weight. As such, it is desired to decrease the wall thickness to 0.065 inches.

Once all the FEA testing of the frame was completed, an assembly of the recumbent bike was created to

determine the required size of our fairing. When the entire bike had been assembled, we realized that someoversights had been made in terms of our gearing system. While the rear derailleur on the bike accounted

for any chain slack in the rear-most chain section, there was no way to maintain chain tension in the front-most portion of our gear system. Without a method of maintaining chain tension, the chain could easily

bounce when going over bumps, causing the chain to fall off the chainrings. As such, a method ofmanaging chain slack needed to be devised.

Competition Venue

Around the same time that the issues with chain management arouse, the venue for our ASME competition

was released to the public. The competition will be held at Ferris State University in Big Rapids, Michigan,and the endurance event will take place on the campus loop as shown below in Figure 5.


10/21

9

Recumbent Testing

During our schools Thanksgiving break the team acquired a recumbent bike that could be used as a test unit

for our geartrain analysis. In addition to providing us with a platform to test our gearing system, therecumbent bicycle also allowed each member to become familiar with the anticipated handlingcharacteristics and dynamics of our human powered vehicle. After riding the bike around The Mall and

Cloke Plaza, the team headed over to the hill by the Student Recreation Center to test hill performance ofthe bicycle. It was found that in order to start from a stop on the steepest hill on campus, a minimum gear

ratio of only 3:1 was required.

With our previous gearing system, we had a three-stage, multi-side power transmission setup. The gearing

system had thirty unique gear ratios ranging from 1.11:1 to 5.72:1. However, if a minimum gear ratio of3:1 ratio was all that was required for any of the hills that we would encounter, the gear train could be

simplified dramatically. Rather than using a multistage gearing system, it was decided to use 1x10 gearing

system to simplify drivetrain construction and chain routing. With this new setup all chain slack could bemanaged using chain pulleys and a rear derailleur, and any possibility for the chain to become unbound wasgreatly reduced.

Not only did our real world testing simplify our gearing system, but it also simplified our drivetrain as well.

Our teams initial decision to use a 700C rear wheel due to the inability to create the required gear ratiosfrom a conventional bicycle drivetrain. However, since a small gear ratio was no longer needed, we could

now return to our initial choice of using 20 inch wheels in the front and rear of the vehicle. Additionally,we could now use a single, large chainwheel to produce the required gear ratio. By using the largest

available chainwheel for recumbent bicycles, an 80 tooth chainwheel, we were able to increase ourmaximum gear ratio to 7.27:1, yielding a maximum speed of 52 mph at a 120rpm pedaling cadence.

When using a 700C rear wheel, the riders seat angle, and consequently the height of the vehicle, was

limited by the diameter of the rear wheel. By switching to the use of a 20 inch rear wheel, the overall heightof the vehicle could be reduced by up to 10 inches, allowing for a smaller projected frontal area and greater

aerodynamic efficiency of the vehicle.


11/21

10

loads specified in the ASME HPVC rule book, ensuring that in the event of a rollover, complete driversafety would be maintained. Our final frame design is shown below in Figure 6:

Figure 6 Final frame design for human powered vehicle.

Our frame now met all specified criteria and effectively accommodated each of our design choices. As

such, this frame design iteration proved to be our final iteration, and is the frame design we have selected to


12/21

11

CFD Verification

Any time a computational technique is used, such as in a CFD program or finite element analysis,

numerical verification must be performed using a simplified case to ensure that the program can accuratelyperform the task, and that the program is being used properly to perform the task. Since we had no previousexperience with Fluent we put extra emphasis on the verification of the flow analysis.

For verification a sphere was used. Since it is a geometric shape with well documented results for drag

coefficients and flow stagnation points, it was the perfect candidate for our first verification analysis.

Verification Methods

Following ANSYS Fluent tutorials, the sphere was created in an outside modeling program and importedinto the ANSYS Workbench. Due to our familiarity with SolidWorks it was chosen to be used for all of our3D CAD modeling. After importing the sphere geometry into the program, the ANSYS Geometry tool was

used to create the wind tunnel. In Fluent, the wind tunnel is created as a large box surrounding the sphere.

The geometry of the sphere is then subtracted out of the wind tunnel volume, leaving a void in the shape of

a sphere. A plane is then created, halving the sphere and the wind tunnel. Since Fluent can account forgeometric symmetries, including the other half of the sphere would result in redundant computations being

performed.

Once the geometry and wind tunnel environment are created, it needed to be meshed. For verification, thestandard ANSYS mesh for CFD is used. Within the ANSYS meshing application, each of the planes is

named. The name symmetry is given to all planes of symmetry and to the walls of the wind tunnel thatare to be modeled without shear. For the verification, all walls are modeled without shear. The end of the

wind tunnel that is to be the entrance of the wind tunnel is titled, velocity inlet. Fluent will recognizethis name as a fluid flow inlet. The exit of the wind tunnel is titled, pressure outlet. Fluent will recognize

this as a pressure relief. The hollowed out half of the sphere is titled as sphere so that is can be easilyrecognized later.


13/21

12

Verification with Temples HPV Fairing Design

Further data verification was done using a design posted by the HPV team from Temple University.

Using their geometric model and running it through a Fluent analysis, a coefficient of drag value obtainedwas 0.23706423. From their design report, the final coefficient of drag that they present is 0.227. Thevalue obtained from our analysis is within 5% of their reported value.

Fairing Iterations and CFD Analysis

Our initial fairing design was based on covering the vehicle with as simple a fairing as possible. The fairingcame to a point at the front end of the vehicle, with an upward inflection as the fairing moves toward the

riders head. After the rider, the curvature of the fairing slopes downward, coming to a round rear section of

the vehicle. This resulted in an improvement over an unfaired recumbent bike, but still had a very highcoefficient of drag. The first fairing iteration is shown below in figure 7:

Figure 7 First fairing design iteration.


14/21

13

The third iteration was aimed to further investigate the effect of curvature on the drag. The fairing was

remodeled to have a downward facing concavity along the entire top portion of the fairing. In doing this,

the coefficient of drag was increased to 0.2878286. From further aerodynamic analysis, it was determinedthat the upward curvature seen in the second iteration resulted in flow separation toward the front of thevehicle. The third iteration decreased the flow separation, and as such increased the pressure related drag

on the front face of the vehicle. As such, we decided to turn our focus toward the second fairing iteration tofurther investigate the effects of flow separation on the coefficient of drag.

A point of interest was identified within the second iteration at the location of the pedals. The heightrestriction of the pedals created a small deviation from a natural curve within the fairing. Removing the

small bump required by having the pedals at a certain height increased the coefficient of drag to0.29550767. This increase in drag was accompanied by a decrease in frontal area. The net result was an

overall higher coefficient of drag area. The bump associated with the pedals may have created a smallamount of turbulent flow which has higher energy and doesnt result in flow separation as easily. Byremoving the bump, the flow transitioned into a more laminar flow and had more flow separation at the rearof the vehicle.

The fifth iteration explored the effect of trailing edge. In the fifth iteration, the fairing length was extended

and gradually tapered to a point at the trailing edge. This resulted in a small decrease in the coefficient ofdrag.

When the time came to start the sixth fairing iteration, the team had just begun the third frame iteration,

featuring a 20 inch rear drive wheel. Since each of the previous fairing iterations were completed using a700C rear wheel, the best of the first five fairing iterations was used as a basis for the sixth fairing iteration.

Design 6 was based off of the fifth fairing iteration, but with a decreased height because the rider sits lowerin the new frame. As a result of the smaller rear wheel, the frontal area of the fairing was decreased from

0.2956009 square meters to 0.2500504 square meters, and a more streamlined and bullet-like shape wasachieved. For this iteration, the coefficient of drag was lowered to 0.19539463.

The final design iteration was based off of design 6 but with a rounded trailing edge instead of one that


15/21

14

To ensure problem-free construction of our aerodynamic fairing, the sixth design iteration was chosen to bethe final fairing design. Up until this point, each of the fairings had been analyzed without wheels using

only first order methods. This simplified analysis is enough to gain a comparative analysis of the

differences between fairing designs, but it cannot accurately put a numerical value on the resistive dragforces that will be seen. To accurately compute the real-world drag forces, wheel volumes were added tosixth fairing iteration. In the Fluent analysis, after the initial solution convergence, turbulence viscosity was

changed to 0.95. Momentum, turbulent kinetic energy, and turbulent dissipation rate were changed fromfirst order to second order solution methods. The Fluent analysis was continued using these new parameters

until convergence was reached again. The final frontal area and coefficient of drag are 0.2497132 square

meters and 0.14969557, respectively. The final Cd*A is 0.037381. The Cd*A for a standard upright bicycleis 0.632. Our fairing produces an amazing 94.1% reduction in drag related forces.

Fairing and Frame Integration

Now that the final design selection has been completed for both the frame and the fairing, we are ready to

start construction of our vehicle. Although the vehicle was broken up into two sections during the design

process, careful procedures have been used to ensure that both the frame and the fairing can be easily

integrated to create the final form of our human powered vehicle.

Throughout the entire frame and faring design process, we have been using our SolidWorks frame andfairing models to ensure that each system can be fully integrated with the other. In order to ensure that the

frame will fit inside of the constructed fairing, each fairing iteration was designed around the most recentframe assembly. Critical dimensions were pulled from the assembly and our own ergonomic measurements

in order to determine fitment of the fairing around the rider and recumbent bike frame itself. Using thesedimensions, each fairing design was lofted to create the most aerodynamically efficient fairing shape. Then,

once each fairing was modeled, the fairing was placed around the vehicle assembly to ensure clearance ofall rotating and stationary components.

By following this procedure with each successive frame and fairing iteration, we have ensured that the


16/21

15

With the design process complete for each of the major components of our human powered vehicle, we areready to begin construction of our aerodynamic fairing. Over the winter break, we plan to start construction

of our fairing plug, and if time allows, finish laying down all composite layers for our aerodynamic fairing.

To construct our fairing, we are going to use a method commonly used to build fairings for human poweredvehicle and velomobiles. Using the fairing that we have modeled in SolidWorks, 2-inch-thick cross

sections will be inserted every 8 inches along the length of the fairing. Each cross section will then be cutso that it takes the exact shape of the fairing at that cross section. Once each section is plotted, the sections

will be printed and glued onto 2 inch polyurethane foam blocks. Then, each foam block will be cut to take

the shape of the contour printout. Once all sections have been formed and cut, they will be assembled tocreate a skeleton of our fairing. A skeleton section from another human powered vehicle is shown below in

Figure 10 to exhibit the construction method we will be using to create our fairing:

Figure 10 Skeleton structure for fairing construction.

Following that, thin strips of polyurethane foam will be laid over the skeleton to produce a solid skin forthe fairing plug. Next, the entire plug will be sanded and formed until the desired shape for our fairing has

been achieved. At this point, we will be able to being laying the composite layers over the plug, creating

th fi i h d f i i d t A fi i h d l f th f ti d h d hi l i th


17/21

16

Once the composite has cured, the fairing can then be cut into top and bottom sections, and the foam

framework used to construct the plug can be removed. Finally, the top and bottom sections will be cut to

allow for the wheels to pass through the fairing, and a smaller, removable section will be created to allowthe driver to enter the vehicle on their own accord.

Upon our return to school in the spring semester, our group will begin to order the bicycle components andmetal stock required to build the recumbent bicycle housed inside of our composite fairing. Like in the

design process, each component will be constructed independent of each other, and when completed, the

fairing and the frame will be integrated to create our human powered vehicle.

Final Thoughts

This project has been an intense learning experience for all involved. Many long afternoons stretching intoevenings have been spent sitting hunched over our laptops trying to figure out why SolidWorks is refusing

to rebuild, or if it really makes more sense to use 20 inch wheels instead of 700C wheels, or if the

differences even matter for what we are doing. We have used our local resources to the best of abilities,

such as going out into the community and talking to bicycle shops such as Roses in downtown Orono, inthe hopes that they could explain to us the intricacies of head tube sizing and bottom bracket spacing, as

well as speaking with professors on campus about different design aspects of our project. We have beenmaking our project known in the community, and we are very gracious to have received sponsorship from

several companies such as PTC, Dassault Systems, and Stuart Marine.

Teamwork has been an integral part of this process, because none of us could have done even a fraction ofthis project without the help of the others. When all you want to do is throw your computer out the window

on the second floor of the library because something isnt working, sometimes all it takes is a teammatelooking over your shoulder and pointing out a simple mistake that you overlooked. We have managed to

keep each other on track, even in the presence of ever-looming midterms, finals, and the hundreds of otherthings that try to steal your attention on a college campus.


18/21

17

References

[1] Accelerating CFD Solutions. ANSYS Advantage. January 2011.

[2] ANSYS Fluent for Vehicle Aerodynamics. Eoescipy. Online Tutorial Series. Youtube.com.

[3] Manan Desai, S.A. Channiwala, H.J. Nagarsheth. Experimental and ComputationalAerodynamic Investigations of a Car. Mechanical Engineering Department, Sardar Vallabhbhai

National Institute of Technology, Surat, Gujarat,INDIA

[4] Marco Lanfrit. Best Practice Guidelines for HandlingAutomotive External Aerodynamics with

FLUENT. Fluent Deutschland GmbHBirkenweg 14a64295 Darmstadt/Germany. 2/9/2005

[5] Wilson, David Gordon, Jim Papadopoulos, and Frank Rowland. Whitt.Bicycling Science.Cambridge, MA: MIT, 2004. Print.


19/21

18

Appendix A: Performance Calculations

Comparative Drag Forces

Aerodynamic Drag Force (lbf)

Speed (mph) Faired Recumbent Recumbent Road Bike Conventional Bike

0 0.00 0.00 0.00 0.00

5 0.41 1.62 1.96 3.65

10 1.62 6.49 7.84 14.61

15 3.65 14.61 17.65 32.86

20 6.49 25.97 31.38 58.42

25 10.14 40.57 49.03 91.29

30 14.61 58.42 70.60 131.46

35 19.88 79.52 96.09 178.92

40 25.97 103.87 125.50 233.70

45 32.86 131.46 158.84 295.77

50 40.57 162.29 196.10 365.15

55 49.09 196.37 237.28 441.83

60 58.42 233.70 282.38 525.82

65 68.57 274.27 331.41 617.11

600

700Drag Force vs. Cruising Speed


20/21

19

Power Calculations

Ka

Wind Speed

(mph)

Wind Speed

(m/s) Ground Speed (mph) Ground Speed (m/s)

Drag Power

(W)

Rolling Drag

Coefficient

0.05 10 4.4704 0 0.0000 0.0000 0.0020

0.05 10 4.4704 5 2.2352 5.0253 0.0020

0.05 10 4.4704 10 4.4704 17.8677 0.0020

0.05 10 4.4704 15 6.7056 41.8775 0.0020

0.05 10 4.4704 20 8.9408 80.4047 0.0020

0.05 10 4.4704 25 11.1760 136.7997 0.0020

0.05 10 4.4704 30 13.4112 214.4126 0.0020

0.05 10 4.4704 35 15.6464 316.5937 0.0020

0.05 10 4.4704 40 17.8816 446.6930 0.0020

0.05 10 4.4704 45 20.1168 608.0609 0.0020

0.05 10 4.4704 50 22.3520 804.0474 0.00200.05 10 4.4704 55 24.5872 1038.0029 0.0020

0.05 10 4.4704 60 26.8224 1313.2775 0.0020

Rolling Drag

(W) Slope Resistance Total Power

Required Input Torque

(Nm)

Required Pedal Force

(lbf) Efficiency Total Force (lbf)

0.0000 0.0000 0.0000 0.0000 0.0000 0.8500 0.0000

3.0689 0.0000 8.0942 0.7030 0.9031 0.8500 1.0625

6.1378 0.0000 24.0055 2.0850 2.6784 0.8500 3.1510

9.2067 0.0000 51.0841 4.4368 5.6996 0.8500 6.7055

12.2755 0.0000 92.6803 8.0496 10.3407 0.8500 12.1655

15.3444 0.0000 152.1442 13.2142 16.9753 0.8500 19.9709

18.4133 0.0000 232.8260 20.2217 25.9772 0.8500 30.5614

21.4822 0.0000 338.0759 29.3629 37.7203 0.8500 44.3768

24.5511 0.0000 471.2441 40.9290 52.5783 0.8500 61.8569

27.6200 0.0000 635.6808 55.2109 70.9251 0.8500 83.4413

30.6888 0.0000 834.7363 72.4995 93.1344 0.8500 109.5699

33.7577 0.0000 1071.7606 93.0858 119.5801 0.8500 140.6824

36.8266 0.0000 1350.1041 117.2608 150.6358 0.8500 177.2186


21/21

20

Gearing Calculations

Outside Diameter Circumference Mile (inches) Rev/Mile Cadence (rpm) RPM at 45mph Mech. Adv. 45

16 50.26548246 63360 1260.507149 120 945.38 7.88

20 62.83185307 63360 1008.405719 120 756.30 6.30

24 75.39822369 63360 840.3380995 120 630.25 5.2526 81.68140899 63360 775.6967073 120 581.77 4.85

27 84.82300165 63360 746.9671996 120 560.23 4.67

28 87.9645943 63360 720.2897996 120 540.22 4.50

29 91.10618695 63360 695.4522203 120 521.59 4.35

RPM at 50 Mech. Adv. 50 RPM at 55 Mech. Adv. 55 RPM at 60 Mech. Adv. 60 RPM at 65 Mech. Adv. 65

1050.42 8.75 1155.46 9.63 1260.51 10.50 1365.55 11.38

840.34 7.00 924.37 7.70 1008.41 8.40 1092.44 9.10

700.28 5.84 770.31 6.42 840.34 7.00 910.37 7.59

646.41 5.39 711.06 5.93 775.70 6.46 840.34 7.00

622.47 5.19 684.72 5.71 746.97 6.22 809.21 6.74600.24 5.00 660.27 5.50 720.29 6.00 780.31 6.50

579.54 4.83 637.50 5.31 695.45 5.80 753.41 6.28

0.00

2.00

4.00

6.00

8.00

10.00

12.00

16 20 24 26 27 28 29

MechanicalAdva

ntage

Tire Diameter (in)


Mech. Adv. 45

Mech. Adv. 50

Mech. Adv. 55

Mech. Adv. 60

Mech. Adv. 65

0.00

2.00

4.00

6.00

8.00

10.00

12.00

16 20 24 26 27 28 29

MechanicalAdva

ntage

Tire Diameter (in)


Mech. Adv. 45

Mech. Adv. 50

Mech. Adv. 55

Mech. Adv. 60

Mech. Adv. 65

Hpvc Capstone Final Report

Documents

Transcript of Hpvc Capstone Final Report