PROJECT CADENCE: HUMAN POWERED VEHICLE by Amoz Eckerson John

PROJECT CADENCE: HUMAN POWERED VEHICLE

by

Adam Christensen

Mordechai Cohen

Amoz Eckerson

John Vesely II

A thesis submitted in partial fulfillment of the requirements for the class of

ME491 – Senior Design II

Milwaukee School of Engineering

28 February 2003

EXECUTIVE SUMMARY

The design of the Project Cadence human powered vehicle (HPV) is composed

of four main areas:

• Energy Model

• Human Power Model

• Aerodynamics

• Frame

Energy Model

An energy model program was developed to analyze a one-hour time trial. This

program calculates the power due to resistive forces, and balances it with human

input power. This program was used to determine the significance of particular

design attributes as well as general trends in reaction to varying external forces.

The model has been verified using actual rider data.

Human Power Model

A technique to model human performance was developed and verified with

actual track data and ergometer testing. It was discovered that human

performance is a non-constant energy process. A linear scaling method is used

that accounts for the differences in human efficiency at different output rates.

When testing this model against rider output measured with both ergometer

testing and actual track performance, the model consistently predicted the

measured output of the rider within 8%.

Aerodynamics

The aerodynamic fairing encloses the rider and vehicle in a shell based on the

NACA 66(4)-021 airfoil profile. The nose of the vehicle is designed to minimize

the high shear region associated with the stagnation point of the fluid flow. The

body is cambered to counteract ground effects. The tail of the vehicle encloses a

majority of the rear wheel, while the front wheel is enclosed in a fairing that

protrudes from the underside of the vehicle.

An aerodynamic analysis tool was constructed to predict the drag area (CDA) of

streamlined shapes based on the skin friction drag of a flat plate. Empirical

relationships were used to correlate the boundary layer flow solution of a flat

plate to three-dimensional shapes. Also, approximations were made of the

additional drag of the wheels and protuberances.

Frame

A frame was designed to accommodate the prone riding position and interface

with the aerodynamic fairing. A structural analysis of this design was performed

to verify its integrity. All of the internal components were specified. A prototype

of the design was constructed as a proof-of-concept.

TABLE OF CONTENTS

Executive Summary ..................................................................................................................................... i Energy Model ........................................................................................................................................ i Human Power Model.......................................................................................................................... ii Aerodynamics ....................................................................................................................................... ii Frame..................................................................................................................................................... iii

Project Statement ........................................................................................................................................1 Background Research.................................................................................................................................3

Aerodynamics ................................................................................................................................8 Human Power .............................................................................................................................10 Mechanical Systems....................................................................................................................14

Specifications..............................................................................................................................................18 Description of the Final Design.............................................................................................................21

Energy Model ..............................................................................................................................33 Human Power .............................................................................................................................34

Scaling Technique................................................................................................................36 Verification of the Scaling Technique..............................................................................38

Design Analysis..........................................................................................................................................41 Aerodynamics ..............................................................................................................................41

Computational Fluid Dynamics / Scale Wind Tunnel Testing...................................42 Three Dimensional Drag Approximation.......................................................................45 Fairing Design Process .......................................................................................................50 Airfoil Selection Process.....................................................................................................51 Fairing Selection Process....................................................................................................54 Verification of Three Dimensional Drag Approximation ...........................................55

Mechanical System......................................................................................................................56 Frame .....................................................................................................................................56

Material Selection..........................................................................................................56 Geometry .......................................................................................................................58

Hanging Body Support.........................................................................................59 Horizontal Elliptical ..............................................................................................62 Triangulated Frame ...............................................................................................65

Finite Element Analysis...............................................................................................72 Drivetrain ..............................................................................................................................73 Tires and Wheels..................................................................................................................75

Design Iterations.........................................................................................................................78 Energy Model Program Iteration Results .......................................................................78

Drag Area.......................................................................................................................80 Rolling Resistance.........................................................................................................81

ii

Grade ..............................................................................................................................82 Wind Speed....................................................................................................................83 Human Power ...............................................................................................................84

Program Structure.......................................................................................................................85 Prototype ......................................................................................................................................89

Conclusions and Future Work................................................................................................................92 Conclusions..................................................................................................................................92 Future Work.................................................................................................................................93

Bibliography ...............................................................................................................................................96 Appendix – Matlab Code ...................................................................................................99

iii

LIST OF FIGURES

Figure 1: Gossamer Albatross...................................................................................................................3 Figure 2: Gold Rush Le Tour [Easy Racers, Inc. 2001]......................................................................4 Figure 3: Sam Whittingham and Varna Diablo [Georgiev. 2002].....................................................5 Figure 4: Matt Weaver and Virtual Edge [Weaver. 2002]...................................................................5 Figure 5: Lars Teutenberg and Whitehawk [RSC Speedbike Bergisch-Gladbach

e.V. 2002].......................................................................................................................................6 Figure 6: Matt Weaver and the Kyle Edge .............................................................................................9 Figure 7: Allan Abbot and his world record holding prone streamliner ........................................11 Figure 8: Human power versus time [NASA. 1964] .........................................................................12 Figure 9: Illustration of body configuration angle ..............................................................................13 Figure 10: Project Cadence vehicle ........................................................................................................21 Figure 11: Vehicle frame..........................................................................................................................22 Figure 12: Rider in prone position, supported at the hips and shoulders ......................................23 Figure 13: Hip and shoulder supports...................................................................................................23 Figure 14: Fork, front wheel, and hydraulic disc brake......................................................................24 Figure 15: Vehicle drivetrain ...................................................................................................................25 Figure 16: Vehicle fairing.........................................................................................................................26 Figure 17: Fairing construction cross-section......................................................................................27 Figure 18: Frame dimensions..................................................................................................................28 Figure 19: Fairing dimensions.................................................................................................................29 Figure 20: Free body diagram .................................................................................................................33 Figure 21: NASA human power curve [NASA. 1964]......................................................................35 Figure 22: NASA human power curve with team rider data points................................................36 Figure 23: Scaling technique....................................................................................................................38 Figure 24: CDA as a function of velocity...............................................................................................44 Figure 25: Local coefficient of shear as a function of length for a flow over a flat

plate ...............................................................................................................................................46 Figure 26: Total skin friction coefficient for a surface area...............................................................47 Figure 27: Torpedo ...................................................................................................................................49 Figure 28: Torpedo with flat tail (TFT) ................................................................................................49 Figure 29: Psarevo - a composite shape made from a torpedo and a TFT ......................................50 Figure 30: Hanging body support design..............................................................................................60 Figure 31: Hanging body support free body diagram ........................................................................60 Figure 32: ALGOR plot of hanging body support displacement ....................................................61 Figure 33: ALGOR plot of the worst stress on the hanging body support design ......................61 Figure 34: Horizontal elliptical design...................................................................................................62 Figure 35: Horizontal elliptical free body diagram..............................................................................63 Figure 36: ALGOR plot of the horizontal elliptical displacement in the z direction...................64

iv

Figure 37: ALGOR plot of the worst stress on the horizontal elliptical design ...........................65 Figure 38: Triangulated frame design ....................................................................................................66 Figure 39: Approximated pedal force vs. crank angle........................................................................68 Figure 40: Chain free body diagram.......................................................................................................69 Figure 41: Chain force vs. crank angle ..................................................................................................70 Figure 42: Free body diagram of triangulated frame design .............................................................71 Figure 43: ALGOR plot of the triangulated frame displacement in the z direction ....................71 Figure 44: ALGOR plot of the worst stress on the triangulated frame design .............................72 Figure 45: Vehicle drivetrain ...................................................................................................................73 Figure 46: Distance traveled as a function of CDA.............................................................................80 Figure 47: Distance traveled as a function of rolling resistance .......................................................81 Figure 48: Distance traveled as a function of grade............................................................................82 Figure 49: Distance traveled as a function of wind speed.................................................................83 Figure 50: Distance traveled as a function of human power ............................................................84 Figure 51: Power as a function of vehicle velocity for a rider on a traditional

upright bicycle..............................................................................................................................87 Figure 52: Power as a function of velocity for a rider on the Project Cadence

vehicle............................................................................................................................................88 Figure 53: Project Cadence prototype...................................................................................................89

v

ACKNOWLEDGMENTS

The authors wish to thank the following companies:

Hayes Brake, LLC

Jason Incorporated

Lincoln Electric

Milwaukee Electric Tool

Modine Manufacturing

NASA / Langley Full-Scale Wind

Tunnel

Rhino 3D

Wheel & Sprocket

The authors wishes to thank the following individuals:

Dr. Allan Victor Abbott

Mrs. Betty Albrecht

Mr. And Mrs. Christensen

Dr. and Mrs. Cohen

Mr. And Mrs. Eckerson

Mr. Roger Hajny

Mr. Bob Jung

Professor Larry Korta

Professor Tom Labus

Ms. Anne Mosgaller

Mr. Dennis Northy

Dr. Vincent Prantil

Mr. Goro Tamai

Mr. And Mrs. Vesely

Mr. Matt Weaver

Mr. Gary Wheeler

Mr. Harry Wozniak

S e c t i o n 1

PROJECT STATEMENT

Project Cadence was inspired by the Dempsey – MacCready Hour Record Prize,

a challenge to travel a distance of 56 miles in a human powered vehicle (HPV) in

one hour powered only by a single rider. The major goal of Project Cadence is to

take the first steps toward the Dempsey – MacCready Hour Record Prize by

designing a vehicle capable of traveling thirty miles in one hour. This distance is

150% of the current rider performance on a traditional upright bicycle.

The scope of the project is to design:

1. A computer model to aid in design decisions

2. An aerodynamic fairing

3. The mechanical systems of the vehicle considering the aerodynamic

parameters

The characteristics of the overall vehicle were inputs to a computer model that

predicted overall performance. It considered the complexity of the human being

as the source of power.

3

S e c t i o n 2

BACKGROUND RESEARCH

There has been a long history of achievement in the development of human

powered vehicles. The following is a list of some of the major milestones.

• Kremer Prizes

o Established in 1959 by Henry Kremer

o $95,000 for the first substantial human powered flight

o First human powered flight across the English Channel

o Won by Paul MacCready’s Gossamer Condor in 1977 and

Gossamer Albatross, respectively (see Figure 1)

Figure 1: Gossamer Albatross

4

• DuPont Prize

o Established in 1983 by the E.I. DuPont Company

o $15,000 for the first human powered land vehicle to travel 65

mph

o Won by Freddie Markham in the Gold Rush in 1986 (see Figure

2)

Figure 2: Gold Rush Le Tour [Easy Racers, Inc. 2001]

• World Human Powered Speed Challenge in Battle Mountain, NV

o Land speed record for human powered vehicles (measured

through a 200 meter speed trap)

o Current record holder is the Varna Diablo II, designed by Georgi

Georgiev and piloted by Sam Whittingham, which went 81 mph

in 2002 (see Figure 3)

5

Figure 3: Sam Whittingham and Varna Diablo [Georgiev. 2002]

o Matt Weaver in the Kyle Edge went 78 mph in 2001 (see Figure

4)

Figure 4: Matt Weaver and Virtual Edge [Weaver. 2002]

6

• Dempsey-MacCready Hour Record Prize

o Established in 1999 to inspire innovation in human powered

vehicles and to promote ultra light, low energy consumption, high

speed human powered transportation

o $25,000 for the first human powered vehicle to travel 90

kilometers (56 miles) in one hour from a standstill

o Lars Teutenberg in the Whitehawk went 82.6 kilometers in July

2002 (see Figure 5)

Figure 5: Lars Teutenberg and Whitehawk [RSC Speedbike Bergisch-Gladbach e.V. 2002]

In addition to the above achievements, the specifications of many record setting

human powered vehicles were collected and compiled (see Table 1)

7

Table 1: Specifications for Different Human Powered Vehicles

Machine Dry

Weight [lb]

Length [in]

Width [in]

Height [in]

Clearance [in] CD Af

[ft2] CDA [ft2] Source

Bean II 0.065 4.790 0.311 Larrington. 2003

Cheetah 0.055 5.450 0.300 Larrington. 2003

CSU 2001 0.110 5.113 0.562 CSU. 2001

Cutting Edge 0.110 2.800 0.308 Larrington.

2003

Gold Rush 0.100 5.000 0.500 Larrington. 2003

Kyle Edge 112.0 19.0 36.0 Beauchamp. 2002

M5 fully faired low racer

0.160 3.122 0.499 Hentschel. 2002

Varna Diablo 2001

59.0 96.0 16.5 30.5 3.0 0.104 2.153 0.224 Whittingham. 2002

Varna Diablo 2002

60.0 96.0 16.0 29.5 0.097 2.056 0.199 Whittingham. 2002

Whitehawk 41.0 18.0 35.0 Beauchamp. 2002

Yellow Bean 0.075 4.470 0.335 Larrington.

2003

8

In preparation for this design project, research was conducted in many related

areas. The following is a survey of the works that have helped shape this project.

Aerodynamics

• Goro Tamai was a member of the dominant MIT Solar Car Team from

1990 through 1995, piloting their vehicles and leading the team to

numerous victories. His book The Leading Edge: Aerodynamic Design of

Ultra-streamlined Land Vehicles [Tamai. 1999] provided valuable

information in the following areas:

o Empirical relations for relating skin friction drag of a flat plate to

common three-dimensional bodies

o Empirical results for increased drag due to wheels and wheel

fairings

o Guidance on vehicle ground clearance

• PABLO [Wauquiez. 1999] is a computer program written in MATLAB

for the analysis of subsonic airfoils. It performs the following functions:

o Viscous (or inviscid) analysis of an airfoil

o Plotting of geometry and pressure distributions

o Calculation of 2-D aerodynamic coefficients

o Location of the transition and separation points for the 2-D flow

field around an airfoil

9

• Matt Weaver is one of the most experienced HPV designers, builders,

innovators, and riders today. He is an engineer who has written

extensively about his ideas and technical issues with HPV design.

Figure 6: Matt Weaver and the Kyle Edge

In his article [Weaver. 1999-2000], Weaver analyzes the effect of wind on

a human powered vehicle. The following are his conclusions:

o Side winds usually produce a net forward propulsion for

streamlined bodies. This is referred to as the sailing effect

o Increasing side winds do produce increased drag, but forward

thrust increases even more (proportional to velocity squared),

resulting in a net gain due to the wind

10

In e-mail conversations with Weaver, he has provided guidance in the

following areas:

o Construction process for the fairing

o Ideas for wind tunnel testing

• Gary Wheeler [Wheeler. 2002] reports that separation is a major cause of

skin friction drag and should be avoided if possible. He also suggested

various ways of using vortex generators on the fairing to reduce drag.

Human Power

• Allan Abbott is the Vice Chair for Academic Affairs at the USC School

of Medicine. He co-authored the book Human Powered Vehicles [Abbott et

al. 1995]. He has held four different world speed records on human-

powered vehicles of his own design, including a prone position

streamliner that set the 200-meter world speed record. He has given the

authors advice regarding rider position.

11

Figure 7: Allan Abbot and his world record holding prone streamliner

o The prone position does not present any restrictions with regard

to breathing as long as the body is supported at the shoulders and

hips. Similarly, a forehead support should be used instead of a

chin support

o Inherent vehicle stability is critical so that the rider does not waste

energy focusing on keeping the vehicle upright

o The unflexed position of the hips and torso requires extensive

training

• The NASA Bioastronautics report [NASA. 1964] provided the following

human power graph (see Figure 8). This relationship proved critical to

the definition of input power for used thrust.

12

Figure 8: Human power versus time [NASA. 1964]

• Reiser II [Reiser et al. 2001] discusses the following points:

o Average power output is greatest in the 130º and 140º body configuration

angles – BCA (see Figure 9)

13

Figure 9: Illustration of body configuration angle

o Power output in the standard upright bicycling position is similar to that

produced in the 130º and 140º body positions

o Familiarity with recumbent riding positions does not lead to higher power

output

• Daniel Too is a faculty member at the Department of Health, Physical

Education, and Recreation at the California State University and has made

numerous contributions in the area of bicycle biomechanics.

o Too discovered [Too. 1991] that anaerobic power and anaerobic capacity

are greatest in the 75º hip position

o Too has found that human power output is greatest at the 90º trunk angle

[Too. 1994]

14

Mechanical Systems

• Cameron’s article [Cameron. 1998-1999] discusses bicycle transmission

and gear efficiencies and simple methods to analyze them.

o Typical bike gear efficiency range is 92.4 – 98%

o Idler gears and more components in a drive system reduce

efficiency

• Chester Kyle was a founder of the International Human Powered Vehicle

Association (IHPVA), director of the 1984 and 1996 United States

Olympic Bicycle projects, and an innovator in human powered land

vehicles. Frank Berto is the former engineering editor for Bicycling

Magazine. Their article [Kyle et al. 2001] discusses the following points:

o Bicycle gear system efficiency increases slightly with power input,

with more marked results at power levels above 250 watts

o Larger sprockets have better efficiency than smaller sprockets

o Most gear systems are 94-95% efficient

o The most significant inefficiency source is sprocket misalignment

• Lafford’s article [Lafford. 2000] discusses bicycle tire attributes and

rolling resistance. He makes the following conclusions:

15

o Larger tire pressure results in a lower rolling resistance

o Less tread and more pliable side walls results in a lower rolling

resistance

o Latex inner tubes reduce the rolling resistance over other inner

tube materials

o Larger tire diameter reduce the rolling resistance

o The rolling resistance coefficient is also dependent on surface

conditions

• Gillespie’s Fundamentals of Vehicle Dynamics [Gillespie. 1992] was used to

analyze rolling resistance attributes. He defines the fundamental equation

for rolling resistance as:

WVCCF srrrr *100

5.2

+=

Equation 1: Equation for rolling resistance of a vehicle [Gillespie. 1992]

o Frr is the force due to rolling resistance

o Crr is the coefficient of rolling resistance based on tire pressure

(from extrapolation, approximately 0.007)

o Cs is the coefficient of rolling resistance based on speed

(extrapolated to be 0.0015)

o V is the vehicle velocity in mph

16

o W is the vehicle weight in lbs

• Wilson discusses drive train efficiencies [Wilson. 1999].

o Derailleur systems tend to be more efficient but are more

susceptible to increased friction losses due to chain misalignment

o There is no consistent trend for gear ratio and efficiency for

various internally geared hub models

18

S e c t i o n 3

SPECIFICATIONS

The following table is a list of the specifications for the design project.

Table 2: Vehicle specifications

Airfoil Profile NACA 66(4)-021 Boundary Layer Characteristics Laminar for 60% of the length

CDA 0.251 ft2

Fairing Kevlar and Nomex Honeycomb

Aerodynamic Fairing

Surface Area 53.95 ft2 Crank Arm Length 165 mm Crank Gear 53 teeth Efficiency > 95% Gear Cassette 30-28-22-16-11 teeth

Drive Train

Wheel Gear 16 teeth

Geometry Triangular Material AISI 4130 Steel Frame

Rider Position Prone

Braking System Single hydraulic disc brake Head Protection DOT certified cycling helmet Safety

Two-way communication system

19

Aerodynamics Enclosed wheel Size 20 in x 2.0 in Tires and Wheels

Tire Type and Pressure Rolling resistance coefficient = 0.0049

Height 31 in (2.58 ft) Length 118 in (9.83 ft) Vehicle Dimensions Width 25 in (2.07 ft) Fairing Weight 17.95 lbs Frame Weight 10.2 lbs Internal Components Weight 16.2 lbs

Vehicle Weight

Total Dry Weight 44.4 lbs

21

S e c t i o n 4

DESCRIPTION OF THE FINAL DESIGN

The Project Cadence Human Powered Vehicle (see Figure 10) is composed of

three major parts: the frame, the internal components, and the aerodynamic

fairing.

Figure 10: Project Cadence vehicle

The frame (see Figure 11) of the vehicle supports the rider, vehicle components,

and fairing. It is constructed of AISI 4130 steel, providing a lightweight, high

strength, minimal deflection structure. The structure is composed of primarily 1

in and 0.5 in outer diameter tubing with 0.035 in wall thickness. The maximum

deflection in the frame is 0.11 in and the maximum stress is about 32,000 psi.

22

Figure 11: Vehicle frame

The rider is suspended above the frame and between the two 20 in wheels in the

prone facedown position (see Figure 12). The rider is supported at the hips and

shoulders (highlighted in red in Figure 13). The shoulder supports are designed

to hold the rider vertically above the frame, and also provide a restraint for the

rider to push against while pedaling. The hip support is fashioned out of foam-

covered walnut, with body contact points at the anterior prominence of the iliac

crests and the anterior pubic ramus [Abbott. 2002]. It allows for hip flexion,

while at the same time providing a solid support for the majority of the rider’s

weight. The rear wheel is located between the legs of the rider, with the pedals

being located behind. There is a forehead support that supports the rider’s head

in a comfortable position.

23

Figure 12: Rider in prone position, supported at the hips and shoulders

Figure 13: Hip and shoulder supports

A battery-powered LCD screen is mounted to the frame directly below the rider’s

head. It provides an illuminated image from a fiber-optic camera mounted in the

nose of the fairing. There is an onboard computer mounted next to the LCD

screen that provides the rider with the speed of the vehicle, the pedal cadence,

and rider heart rate. A battery-powered two-way radio is mounted to the frame,

24

providing a communication link between rider and support crew. The push-to-

talk button is mounted on a handle bar. The rider speaks through a small

microphone and listens via an inner-ear headset.

The tires are 20 in outside diameter and are enclosed by a composite disk that

surrounds the wheel and tire. There is a front hydraulic disk brake and a gear

shifter is integrated with the brake lever. The steering mechanism is mounted

directly to the front fork. Figure 14 shows the details of this front assembly.

Figure 14: Fork, front wheel, and hydraulic disc brake

The drive train (see Figure 15) is located at the rear of the vehicle. Its design is

simple and compact to minimize chain length, reduce chain alignment problems,

25

and improve efficiency. It is composed of 165 mm crank arms, a crank gear, a

chain tensioner, four intermediate reduction gears, a derailleur, and the wheel cog.

Figure 15: Vehicle drivetrain

The aerodynamic fairing (see Figure 16) encloses the rider and vehicle in a shell

designed for a drag area of 0.25 ft2. It is based on the NACA 66(4)-021 airfoil

profile having a maximum width of 2.07 ft and maximum height of 2.58 ft. The

nose of the vehicle is pointed to minimize the high shear region associated with

the stagnation point of the flow. The body is cambered in the side view, which

provides a small element of lift, reducing the downforce inherent with vehicles

traveling in proximity to the ground. The tail is shaped to enclose a majority of

the rear wheel without excess protuberances. There is a faired front wheel, which

protrudes from the underside of the vehicle and provides the wheel enclosure.

26

The tires protrude from their fairing enclosures 1 inch. The overall ground

clearance of the vehicle is three inches.

Figure 16: Vehicle fairing

The fairing is constructed of a Kevlar and Nomex composite (Kevlar was chosen

over carbon due to safety reasons). There are 2 layers of 5 oz/yd2 Kevlar (0.01 in

thickness each layer) surrounding a 0.21 in Nomex honeycomb core (1.8 lb/ft3)

as shown in Figure 17. The total thickness of the fairing is 0.25 inches and

weighs just under 18 lbs.

27

Figure 17: Fairing construction cross-section

28

Figure 18 shows the primary dimensions of the vehicle frame. All dimension

lengths are in inches.

Figure 18: Frame dimensions

Figure 19 shows the primary dimensions of the aerodynamic fairing. All

dimension lengths are in inches.

29

Figure 19: Fairing dimensions

30

Table 3 is the bill of materials for construction of the frame. Items needed, the

amount needed, and pricing came from a variety of sources.

Table 3: Frame bill of materials

Item Description Price [$] Per Unit Units Total

+ 20% Cost [$]

4130 Steel tube 1 in OD x 0.035 in WT 23.86 8 ft 1 1.2 28.63

4130 Steel tube 1 in OD x 0.035 in WT 11.50 3 ft 1 1.2 13.80

4130 Steel tube 0.5 in OD x 0.035 in WT 16.93 5 ft 3 3.6 60.95

4130 Steel tube 0.75 in OD x 0.035 in WT 4.25 1 ft 1 1.2 5.10

Front fork Fit for 20 in wheel 17.50 1 fork 1 1.2 21.00

TOTAL 129.49

31

Table 4 is the bill of materials for the internal components of the vehicle. Items

needed, the amount needed, and pricing came from a variety of sources

[BikeParts USA. 2003, Cambria Bicycle Outfitter. 2003, Irion Lumber

Company. 2003, Minnesota Human Powered Vehicle Association. 2003].

Table 4: Internal components bill of materials


+ 20% Cost [$]

Shimano Ultegra 6500 crank set

165 mm x 53 T, nickel plated SG-X

chain rings 89.00 each 1 1.2 106.80

Left crank arm 165 mm 23.00 each 1 1.2 27.60

Shimano LX HG-50 IG cassette 30-28-22-16-11 T 19.00 each 1 1.2 22.80

Chain 116 links 10.00 each 2 2.4 24.00

Front hub 27.00 each 1 1.2 32.40

Rear hub 38.00 each 1 1.2 45.60

Clipless pedals CrMo spindle 39.00 pair 1 1.2 46.80

Threadless headset 25.00 each 1 1.2 30.00

Polyethylene foam pipe insulation ¾ in thick 4.74 6 ft 1 1.2 5.69

Walnut hip support Custom machined 100.00 each 1 1.2 120.00

Hayes hydraulic disc brake 74 mm 6” rotor 89.00 each 1 1.2 106.80

Velocity Deep-V 20 in wheel

24 mm wide, 32 mm deep aero rim 55.00 each 2 2.4 132.00

Shimano 105 5500 rear derailleur

11 T pulleys, 9 speed compatible 34.00 each 1 1.2 40.80

Shimano shift / brake combo 65.00 each 1 1.2 78.00

ACS RL Edge 20” x 2.0” tire

100 psi, Crr1 = 0.0049 24.00 each 2 2.4 57.60

Continental inner tubes 20” x 1.5-1.75” $7.00 each 2 2.4 16.80

Handlebars 26 mm clamp diameter 19.00 pair 1 1.2 22.80

TOTAL 916.49

32

Table 5 is the bill of materials for construction of the fairing. Items needed, the

amount needed, and pricing came from a variety of sources [Fibre Glast

Developments Corp. 2003, Howard. 2003, Weaver. 2002-2003].

Table 5: Fairing bill of materials


+ 20% Cost [$]

Kevlar 49 cloth 5 oz/yd2, 0.01” thick, s.g. = 1.45 41.80 m2 20 24 1003.20

Nomex Honeycomb Core

1.8 lbf/ft3, 0.21” thick 127.68 m2 6 7.2 919.30

System 2000 Resin Good for Kevlar, low toxicity 64.95 gal 1 1.2 77.94

System 2000 Hardener Long pot life 24.95 gal 1 1.2 29.94

Mold polish step 1 14.95 lbf 1 1.2 17.94

Mold polish step 2 14.95 lbf 1 1.2 17.94

Parting wax 8.95 24 oz 24 28.8 257.76

Release film 9.45 quart 1 1.2 11.34

Vacuum bag connector 39.95 each 2 2.4 95.88

Vacuum tubing 1.00 foot 1 1.2 1.20

Bagging film Nylon 5.95 yd2 8 9.6 57.12

Breather / Bleeder cloth 7.95 yd2 8 9.6 76.32

Release ply 12.95 yd2 8 9.6 124.32

Seal Tape 6.95 roll 1 1.2 8.34

TOTAL 2698.54

TOTAL VEHICLE COST = $3744.52

33

Energy Model

The energy model is a system balance determined by the free body diagram (see

Figure 20). Equation 2 summarizes the components of the system balance by

stating that the human supplied power is used entirely to counter forces on the

system and provide acceleration.

Figure 20: Free body diagram

2 22 2.5( ) ( 3.24 ) sin

2 2Human Power System Power Demand Acceleration Velocity

iDef wind o s

V VC AP V V V N f f V W MVx

ρη φ − − − + + + = − = ×

Equation 2: Energy model equation

34

The following are the components of the System Power Demand:

• Aerodynamic Drag

• Rolling Resistance

• Force of Vehicle Weight Climbing Up An Incline

Each of these components as well as the details about each term in Equation 2

will be discussed in greater detail in the Program Structure section.

Human Power

The Energy Model analyzes the mechanical energy that the human rider can

supply the vehicle to overcome the resistive forces. The nature of a human being

as an energy source can be seen in Figure 21.

35

Figure 21: NASA human power curve [NASA. 1964]

Figure 21 shows the maximum time that an average “healthy man” can sustain a

constant output rate on an ergometer. It also shows that a human being is more

efficient at lower output rates.

This curve was calibrated by testing the team rider in the output range of 160 to

600 watts and comparing the data to the “healthy man” curve (see Figure 22).

36

Figure 22: NASA human power curve with team rider data points

The curve fit through the data points for the rider represents the capacity of rider

to sustain a constant output rate until he is fatigued. It was necessary to adapt

this curve to predict rider performance at different output rates throughout the

course of a time trial. To accomplish this, a scaling technique was formulated and

tested.

Scaling Technique

The scaling technique can best be described with an example.

37

1. The process starts with the fatigue curve, P = 468 t –0.2 determined for the

standard rider

2. An initial output rate is chosen, in this case 300 watts

3. At this level, the curve and equation show that the rider is capable of

sustaining this rate for 9.2 minutes prior to exhaustion

4. If the rider maintains this rate for 4.6 minutes, he has only used ½ of his

potential

5. With the rider ½-way to exhaustion, he switches his output rate to 200

watts

6. The original curve shows that the fully rested rider could sustain an

output rate of 200 watts for 70.2 minutes. However, the rider is ½-way

to exhaustion, so the time that the rider can now maintain 200 watts is

predicted to be 35.1 minutes (½ of 70.2).

Figure 23 shows this technique graphically.

38

Figure 23: Scaling technique

Verification of the Scaling Technique

To verify the scaling technique, a series of time trials were performed with the

team rider on an ergometer. Two of the time trials followed an identical process

described in the example above. The third test involved a series of four output

rate adjustments over the course of the trial. Table 6 highlights the results of

these experiments.

39

Table 6: Verification of the scaling technique

Test 1 Test 2 Test 3 R1 Initial Output Rate (Watts) 480 600 320

T(R1) Max Time at R1 (minutes) 1.0 0.302 5.4 t1 Test time (minutes) 0.5 0.25 1.0 k1 Scaling Factor k1 = 1 – t1/T(R1) 0.500 0.172 0.815 R2 New Output Rate (Watts) 320 480 240

T(R2) Original Max time at R2 (minutes) 5.4 1.0 25.0 T2 Scaled time T2 = k1 x T(R2) 2.7 0.172 20.37 t2 Time achieved by rider (minutes) 2.62 0.200 9.0 k2 Scaling factor k2 = k1 - t2/T(R2) - - 0.455 R3 New Output Rate (Watts) - - 160

T(R3) Original Max time (minutes) - - 176.65 T3 Scaled time T3 = k2 x T(R3) - - 80.4 t3 Time achieved by rider (minutes) - - 50 k3 Scaling factor k3 = k2 – t3/T(R3) - - 0.172 R4 New Output Rate (Watts) - - 240

T(R4) Original Max time (minutes) - - 25 T4 Scaled time T4 = k3 x T(R4) - - 4.3 t4 Time achieved by rider (minutes) - - 4.0

ttotal Total trial time (minutes) 3.12 0.45 64 Ttotal Total theoretical time (minutes) 3.20 0.40 64.9

Difference in total time 2.56% 11.1% 1.45%

Tests 1, 2, and 3 show that the scaling technique developed is valid for predicting

human performance and that the accuracy of the model predictions increases as

the total trial time increases.

41

S e c t i o n 5

DESIGN ANALYSIS

Aerodynamics

Aerodynamic drag is calculated using Equation 3:

2

21 VACF DDrag ρ=

Equation 3: Equation for aerodynamic drag

where CD is the drag coefficient, A is the characteristic area, ρ is the density of air,

and V is the velocity.

The important design element is CDA – the coefficient of drag acting over the

characteristic vehicle area. Both the drag coefficient and the characteristic vehicle

area are dependent on vehicle size and shape. The goal is to design for the lowest

possible drag area – CDA.

42

Computational Fluid Dynamics / Scale Wind Tunnel Testing

There are two traditional methods for evaluating the aerodynamic characteristics

of a three dimensional streamlined shape:

1. Computational Fluid Dynamics (CFD)

2. Scale Wind Tunnel Model Testing

Both of these methods could be used to determine the CDA of the vehicle. In

addition, these methods would allow for the study of such effects as

protuberance drag and camber (topics discussed later in the Three Dimensional

Drag Approximation section), as well as the comparison of different fairing

designs.

The Milwaukee School of Engineering does not currently have CFD capabilities,

and therefore this method could not be used to evaluate different fairing designs.

The university does however have a one-sixth-scale wind tunnel and the testing

of fairing designs in it was considered. The accuracy of this testing can only be

assured if the Reynolds number (see Equation 4) is preserved when scaling.

Re VLρµ

=

Equation 4: Equation for the Reynolds number of an object moving in a fluid

where ρ is the density of the fluid, V is the velocity of the object, L is the length

of the object, and µ is the viscosity of the fluid.

43

The following calculations show that to preserve the Reynolds number on the

one-sixth-scale model, the wind tunnel would have to be operated at a speed of

about 180 mph to simulate 30 mph of the full-scale vehicle.

( )( )33

63

7

2.38 10 44 9.83Re 2.75 10

3.74 10

slug ft ftsftfts

−

−

× = = ×

×

For the above calculation, the velocity of the full size vehicle was 30 mph, which

is 44 ft/s, and the length of the full size vehicle was 118 in, which is 9.83 ft. The

velocity required for a one-sixth-scale model, based on the equivalent Reynolds

number is calculated as follows.

( )33

63

7

2.38 10 1.6392.75 10

3.74 10

scaleslug V ftft

fts

−

−

× × =

×

For a one-sixth-scale model, the length would be 19.67 in, which is 1.639 ft.

From the above calculation, the scale velocity would have to be 263.7 ft/sec or

about 180 mph. The maximum possible speed of the MSOE wind tunnel is

approximately 90 mph.

If the one-sixth-scale model was tested at 90 mph, this would scale to a full-scale

vehicle road speed of 15 mph, which is less than half the project goal. In

addition, any data taken from testing at 15 mph would be suspect in terms of

applying it to the full-scale vehicle. This is because CDA varies as a function of

speed (and consequently Reynolds number) as can be seen from below.

44

CDA as a Function of Velocity

0

0.005

0.01

0.015

0.02

0.025

0 5 10 15 20 25 30 35

Velocity [ft/sec]

C DA

[ft2 ]

Figure 24: CDA as a function of velocity

Even if the data collected at 15 mph were meaningful for predicting drag at

higher speeds, the drag on the one-sixth-scale model would be so small that

measurement would be difficult and any errors in the measurement could be a

large percentage of the total.

45

Three Dimensional Drag Approximation

Determining the CDA of a three dimensional streamlined shape is a difficult

process, because the drag is predominantly skin friction (around 90% for

streamlined shapes [Tamai. 1999]). It is possible to solve for the skin friction of

a flat plate and then use empirical relations to relate this to select three-

dimensional bodies. Below is the process used.

1. Skin friction drag over a flat plate was calculated by integrating the shear

stress between the air and the surface of the vehicle over the entire

vehicle surface

2. The local skin friction coefficient (Cτ) is the shear force per unit surface

area [Tamai. 1999]. For flow over a flat plate, Cτ is related to Reynolds

number for both laminar and turbulent flow:

,laminar 1/ 2

0.664Rex

Cτ =

Equation 5: Local skin coefficient for a laminar flow

,turbulent 1/5

0.0576Rex

Cτ =

Equation 6: Local skin coefficient for a turbulent flow

46

where Rex is the local Reynolds number. Figure 25 shows the local skin

friction coefficient as a function of length with transition from laminar to

turbulent flow imposed at 50% of the length

Figure 25: Local coefficient of shear as a function of length for a flow over a flat plate

3. The total skin friction coefficient (Cf,flat) is calculated by integrating the

individual local skin friction coefficients over the surface area of the plate,

taking into account regions of laminar and turbulent flow:

47

, ,laminar ,turbulent0

t

t

x l

f flatx x x

C C dx C dxτ τ= =

= +∑ ∑

Equation 7: Total skin friction coefficient for a flat plate

where xt is the location of transition from laminar to turbulent flow

4. Figure 26 shows the local skin friction coefficient over the entire surface

area. The volume under the curve is the total skin friction coefficient for

the entire surface area

Figure 26: Total skin friction coefficient for a surface area

5. Minimizing the volume under the curve translates into drag reduction.

There are two methods in which this can be achieved: 1) to extend the

region of laminar flow and minimize the region of turbulent flow, or 2) to

48

minimize the high shear force stagnation region by making the body

narrower and more pointed at the front

6. The following empirical relations were constructed from wind tunnel data

from many aerodynamic research centers, and showed consistent results

[Tamai. 1999]. They state the total drag coefficient for the given three

dimensional shapes are composed of the skin friction of flow over a flat

plate, a small supervelocity component, and an even smaller separation

pressure component

[ ], Skin Friction Supervelocity Separation Pressured wetC = + +

Equation 8: Equation for the drag coefficient of a three dimensional shape

The supervelocity component of drag is due to the acceleration of the

flow around the body. The separation pressure term adds a component

of drag due to the pressure gradient on the vehicle beyond the maximum

thickness.

7. For a torpedo shape, the following empirical equation for the drag

coefficient applies

+

+=

35.1

,, 75.11LD

LDCC flatfwetd

Equation 9: Equation for the drag coefficient of a torpedo shape [Tamai. 1999]

49

Figure 27: Torpedo

For a torpedo with a flat tail (TFT) shape, the following is the empirical

equation for the drag coefficient

+

+=

65.1

,, 195.11LD

LDCC flatfwetd

Equation 10: Equation for the drag coefficient of a torpedo with a flat tail (TFT) [Tamai. 1999]

Figure 28: Torpedo with flat tail (TFT)

In each of these relations, D is the maximum body diameter and L is the

vehicle length.

Various solar car teams, in designing their vehicles, have used these

relationships. CDA predictions made by these relationships have been

reported to agree well with computational fluid dynamics results and even

better with actual drag measurements taken from full-size vehicles

[Tamai. 1999].

50

8. In an effort to reduce wetted area, add camber to the vehicle, and enclose

the rear wheel, a new shape dubbed Psarevo (see Figure 29) was created,

which is a combination of a torpedo and a TFT

Figure 29: Psarevo - a composite shape made from a torpedo and a TFT

Fairing Design Process

The composite fairing shape was constructed by using three airfoil cross sections:

1. Plan (top) view

2. Upper surface in the side view

3. Lower surface in the side view

51

The lower surface was modified by replacing the rear portion of the airfoil profile

(all points of the airfoil occurring behind the maximum thickness) with the

maximum thickness. This provides enclosure for the rear wheel.

Airfoil Selection Process

Airfoil profiles were selected based on the following criteria:

1. Symmetry in plan view

2. Low drag

3. Laminar flow for a large percentage (greater than 50%) of chord length

4. Ability to fit the rider and all internal components

Based on the above criteria, the following airfoil profiles [Selig. 2000] were

chosen for comparison:

• NACA 66(4)-021

• NASA / Langley / Somers-Selig-Maughmer NLF(1)-0115

• NASA / Langley / Somers-Maughmer NLF(1)-1015

• NASA / Langley / Viken NLF(1)-0414F

• University of Alberta / Marsden UA 79-SF-187

52

In order to satisfy the symmetry criterion, some airfoil profiles were modified by

mirroring the upper surface of a nonsymmetrical airfoil to create a symmetrical

one in plan view.

The 2-D drag coefficient, percent laminar flow, and separation point were

determined for each symmetric airfoil profile using a two-dimensional potential

flow solution at a Reynolds number of 5 x 106. Laminar flow and separation

point are a percent of chord length. Head, shoulder, and feet clearance are in

inches.

NACA 66(4)-021 2-D CD 0.0044

Laminar Flow 60.1 Separation Point

Fit Yes Head Clearance 12.3

Shoulder Clearance 25.3 Feet Clearance 29.7

NLF(1)-0115 2-D CD 0.0049


Fit No Head Clearance 14.8


53

NLF(1)-1015

2-D CD 0.0047 Laminar Flow 59.8

Separation Point 98.0 Fit Yes

Head Clearance 16.8 Shoulder Clearance 29.8

Feet Clearance 24.8

NLF(1)-0414F 2-D CD 0.0035


Fit No Head Clearance 17.8


UA 79-SF-187 2-D CD 0.0041


Fit Yes Head Clearance 15.1


The 2-D CD was calculated using PABLO [Wauquiez. 1999], an open source

computer program written in MATLAB for the analysis of subsonic airfoils.

From the above five airfoil profiles, only three represent viable options since two

do not satisfy the fit criterion.

54

Fairing Selection Process

Since the three remaining airfoil profiles each represent a viable choice for the

fairing design, a determination needed to be made as to which to use for the

vehicle fairing. Table 7 shows how it was decided to use the NACA 66(4)-021

airfoil profile to create the Psarevo shape described in the Fairing Design Process

section above.

Table 7: Comparison of aerodynamic characteristics for the fairing selection process

NACA 66(4)-021 NLF(1)-1015 UA 79-SF-187

Frontal Area [ft2] 3.75 4.27 4.63

Surface Area [ft2] 53.95 57.83 58.25

CDA [ft2] 0.251 0.260 0.267

The CDA values in Table 7 were calculated by approximating each fairing as a

TFT and using Equation 10 to find the CDA. Added to that value was an

empirical-based value for the protuberance drag of two faired spinning wheels

[Tamai. 1999]. Since a fairing based on a NACA 66(4)-021 air foil profile has a

lower CDA as well as smaller frontal and surface areas, it was therefore selected

over the two other airfoil profiles.

55

Verification of Three Dimensional Drag Approximation

It should be noted that the CDA values obtained using the methods outlined in

the previous sections are on the order of other streamlined human powered

vehicles (see Table 1). This would indicate that the Three Dimensional Drag

Approximation method is valid. Further testing of the Psarevo shape using CFD

or wind tunnel models will hopefully show that the predicted values are

reasonable.

56

Mechanical System

The mechanical system consists of three primary components:

• Frame

• Drivetrain

• Tires and Wheels

Each of these components will now be discussed in detail to highlight the design

process.

Frame

Material Selection

Several material types were investigated including different types of aluminum

and steel. The frame material was chosen based on the criteria listed below:

• Physical properties

o High modulus of elasticity – a very stiff material is important in

order to have efficient power transfer from the rider to the pedals

57

o High yield strength – a very strong material is important in order

to accommodate the high stresses that can be generated

o Ductility

• Weldability

• Availability

• Cost

The different materials evaluated can be found in Table 8.

Table 8: Frame materials

Material ρ [lbf/in3] E [psi] UTS [psi] Stiffness / Weight

Strength / Weight

Aluminum 2011-T6 0.102 1.02E+07 39200 1.00E+08 3.84E+05

Aluminum 2025-T6 0.102 1.03E+07 37000 1.01E+08 3.63E+05

Aluminum 2014-T4 0.101 1.05E+07 42100 1.04E+08 4.17E+05

AISI Steel 4130 0.284 2.97E+07 66700 1.05E+08 2.35E+05

Aluminum 2024-T6 0.1 1.05E+07 50000 1.05E+08 5.00E+05

Aluminum 2024-T86 0.1 1.05E+07 63800 1.05E+08 6.38E+05

Aluminum 2218-T61 0.101 1.08E+07 44200 1.07E+08 4.38E+05

Aluminum 2090-T83 0.0936 1.10E+07 75400 1.18E+08 8.06E+05

58

Although some heat-treating processes can enhance the properties of aluminum,

it has been advised by consultants that it would be much easier to weld steel

[Jung. 2002-2003]. Therefore, the frame will be built to the design criteria using

AISI 4130 steel.

Geometry

Several designs were looked at as possible frame configurations. The following

were the criteria for frame design:

• Overall weight less than 15 lbf

• Attachment of the fairing

• Rider ergonomics

• Maximum deflection less than 0.15 inch in the vertical direction

• No yielding

• Factor of Safety ≥ 2

Table 9 shows how each of the three designs analyzed performed against the

design criteria.

59

Table 9: Performance of different frame designs

Hanging Horizontal Elliptical Triangulated

Overall Weight [lb] 48.5 44.6 11.8

Fairing Attachment Excellent Excellent Good

Factor of Safety 2.38 1.4 2.07

Maximum Vertical Deflection [in] 1.18 0.55 0.11

No Yielding Pass Pass Pass

Hanging Body Support

The hanging body support design consists of one main beam that follows the

contour of the fairing so that a sling could be hung from it to support the rider

(see Figure 30 and Figure 31).

60

Figure 30: Hanging body support design

Figure 31: Hanging body support free body diagram

• Advantage – easy to attach a fairing along the length of the upper support

• Disadvantage – failed the maximum deflection and weight criterions (see

Figure 32)

61

Figure 32: ALGOR plot of hanging body support displacement

In Figure 33, the worst stress on the frame is shown.

Figure 33: ALGOR plot of the worst stress on the hanging body support design

62

Horizontal Elliptical

The design consists of two beams that span the entire length of the vehicle. A

cross member is located at the hips and shoulder in order to provide support for

the rider (see Figure 34).

shoulder support

hip support

main support beams

front

rearwheel

wheel

Figure 34: Horizontal elliptical design

• Advantages – allows for easy attachment of the fairing to the frame

• Disadvantage – too heavy when compared to the triangulated design

A free body diagram is presented in Figure 35.

• Design Assumptions

o No forces due to tension in the chain or pedal forces were added

o Weight distribution would be concentrated at the hips.

63

The analysis performed showed that it was not necessary to continue with more

detailed considerations as it failed the design criteria under the loadings from the

weight of the rider only.

Figure 35: Horizontal elliptical free body diagram

In Figure 36, the maximum displacement in the z direction is shown to be greater

than the design criterion of 0.15 in.

64

Figure 36: ALGOR plot of the horizontal elliptical displacement in the z direction

In Figure 37, the worst stress was found to be such that the factor of safety was

1.4; this was below the design criteria of 2.

65

Figure 37: ALGOR plot of the worst stress on the horizontal elliptical design

Triangulated Frame The design consists of a triangulated tubing layout similar to a traditional upright

bicycle, but modified to fit the rider in the prone position (see Figure 38).

66

Figure 38: Triangulated frame design

The frame was then modeled in ALGOR.

• Rider Weight

o The weight of the rider is 200 lbf

o This weight was multiplied by a factor of 3 in order to

approximate a dynamic loading on the frame

o The weight is distributed across the frame by two contact points

located at the hips and at the shoulders. It was estimated that

two-thirds of the rider weight would be carried by the hips and

the remaining one-third of the body weight would be carried by

the shoulders

• Pedaling Forces

67

o The rider is assumed to sustain a power output of 200 W for 1

hour. The calculation below shows how the average force on the

pedals is calculated

200 147.5

1min 2 (6.5 ) 180min 60sec 12147

2

65

P T

W ft lbf T

rev in ftFrev inft lbf

F lbf

ω

ω

π

=

= − =

− =

=

o There is a factor of ½ built into the equation that accounts for

the cyclic nature of a pedal stroke

This value, however, is only an average value. Due to the nature of the muscles

in the leg, it is possible to model the force into the pedal as a half sine wave (see

Figure 39).

68

Approximated Pedal Force vs. Crank Angle

0.00

50.00

100.00

150.00

200.00

250.00

0 50 100 150 200 250 300 350

Crank Angle

Peda

l For

ce (l

bf)

Figure 39: Approximated pedal force vs. crank angle

From Figure 39, it can be seen that when the average force is 65 lbf, the

maximum force applied by the rider is approximately 200 lbf.

The force on the chain is larger than that on the pedal because it has a shorter

moment arm (see Figure 40).

69

Figure 40: Chain free body diagram

1 1

2 2

21 2

1

2

2

100200165

330

pedal

chain

pedal chain

T F L

T F LT T

LF FL

mmlbf Fmm

F lbf

=

==

=

=

=

Figure 41 shows the chain force as a function of crank angle.

70

Chain Force vs. Crank Angle

0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

0 50 100 150 200 250 300 350

Crank Angle

Cha

in F

orce

(lbf

)

Figure 41: Chain force vs. crank angle

The force on the frame is larger than that of the rider pushing on the pedal. In

the ALGOR model it was approximated to be 350 lbf.

Since the design has the rider lying down with the head forward, a shoulder

restraint was added in order to prevent the rider from sliding forward and losing

power to the pedals. This force is approximated to be equal in magnitude but

opposite in direction of the force applied by the rider to the pedals.

A layout of the boundary conditions and loadings on the triangulated frame

design is shown in Figure 42.

71

Figure 42: Free body diagram of triangulated frame design

This frame geometry is acceptable to both the maximum deflection and the no

yielding criterions. The maximum deflection is 0.14 in (see Figure 43) and the

maximum stress is 37286 psi (see Figure 44).

Figure 43: ALGOR plot of the triangulated frame displacement in the z direction

72

Figure 44: ALGOR plot of the worst stress on the triangulated frame design

Finite Element Analysis

All finite element analysis (FEA) calculations were performed with ALGOR.

The details of the triangulated frame are presented here.

Parameter Model Data

Type of FEA Element Beam Number of Elements 330

Material Data Steel 4130 (built into ALGOR)

73

Drivetrain

The drivetrain was designed to be as compact as possible, while still providing the

flexibility of multiple gears (see Figure 45). By situating the crank gear, cassette,

and rear wheel gear / hub in proximity to each other, a significant reduction in

chain length was realized. This resulted in weight savings, and more importantly,

increased the transmission efficiency.

Figure 45: Vehicle drivetrain

There are two chains that drive the system. The first rides along the 53-teeth

crank gear, through a chain-tensioning device and around the 11-teeth gear of the

cassette. The second chain runs along the 16-teeth rear wheel cog, through a

derailleur, and around any one of the four gears composing the cassette. In the

highest gear (30-teeth cassette gear) and at a pedal cadence of 60 rpm, the vehicle

74

will travel at 32 mph. The drivetrain specifications and gearing characteristics are

shown in Table 10 and Table 11, respectively.

Table 10: Drivetrain specifications

Drivetrain Specifications

Crank Arm 165 mm

Crank Gear 53 T

Cassette / Crank Gear 11 T

Cassette Gear 1 16 T




Rear Wheel Gear 16 T

Rear Wheel 20 inch OD

Table 11: Drivetrain characteristics

Drivetrain Characteristics

Drivetrain Gear Ratio Vehicle Speed [mph]

Gear 1 4.82 17.2

Gear 2 6.63 23.7

Gear 3 8.43 30.1

Gear 4 9.03 32.2

The vehicle speeds reported in Table 11 are at a pedal cadence of 60 rpm.

75

Tires and Wheels

With the overall vehicle dimensions being restricted due to the aerodynamic

specifications outlined in the sections above, it was therefore necessary to use

wheels no larger than 20 inches in diameter. There are two main characteristics

that the tires and wheels contribute to the design:

• Rolling resistance

• Weight

In general, tire diameter and coefficient of rolling resistance (Crr) are inversely

related [Lafford. 2000]. The smallest diameter tires with the lowest Crr are

manufactured specifically for solar car racing. The use of these tires could reduce

the Crr by a factor of about 2, which would result in a significant reduction in

resistance (see Table 12). However, using solar car tires requires the use of solar

car wheels because solar car tires are tubeless (unlike standard bicycle tires). Solar

car wheels weigh more than bicycle wheels, resulting in an increase in vehicle

weight enough that almost no benefit would be realized (see Table 13). For this

purpose, Deep-V wheels made by Velocity were chosen for their low weight and

small size, and ACS RL Edge tires were chosen for their relatively low value for

Crr.

76

Table 12: Tire comparison [Tamai. 1999]

Type Manufacturer Model Diameter [in]

Width [in]

Weight [lbf] Crr1

Bicycle Avocet Freestyle 20 1.75 0.805 0.0052

Bicycle ACS RL Edge 20 1.75 0.849 0.0049

Solar Dunlop Solar Max 17 4 0.0031

Solar Bridgestone Ecopia EP80 14 2.25 3.0 0.0027

Solar Bridgestone Ecopia 16 2.25 0.0027

Solar Bridgestone Ecopia 19 2.25 0.0027

Solar Michelin Radial 16 2.56 0.0023

77

Table 13: Wheel specifications

Type Manufacturer Model Diameter [in]

Width [in]

Weight [lbf]

Bicycle GH Craft Carbon Fiber 20 1.75 1.96

Bicycle Front 26 1.6

Bicycle Rear 26 2.25

Motorcycle 16 2.15

Solar NGM 6061 Aluminum 14 2.25

Solar GH Craft Carbon Fiber 14 2.25 2.25

Solar GH Craft Carbon Fiber 16 2.25 2.65

78

Design Iterations

While the specifications of the project as described lead to a vehicle capable of

traveling 30 miles in one hour, it is important to note which attributes have the

most significant effect on the total distance traveled and which are not as serious.

If some need to be infringed, that may be possible while still attaining the design

goals.

Energy Model Program Iteration Results

Table 14: Energy model program iteration results

Scenario CDA Crr Weight Wind Power Distance Up Wind

Down Wind Notes

[ft2] [lbf] [mph] [mile] [ft/sec] [ft/sec] 1 3.4 0.005 220 10 Standard 18.7 22.2 32.8 Standard Bicycle Race Verification 2 0.2 0.005 200 5 Standard x 2 45.9 67.2 67.4 HPV verification Numbers 3 0.3 0.005 250 10 Standard / 2 32.9 48 48.6 Specified Cycle Attributes 4 0.3 0.005 250 0 Standard 31.8 46.4* 47* Trend for viewing grade 10 degrees * applies to direction of incline as wind

• The program results correlate to actual time trials for the rider on a

traditional upright bicycle

79

• The program results correlate to published data for professional human

powered vehicles

• Under wind conditions, the program indicates that the rider should make

up time when going downwind

• For grade conditions, the program indicates that the rider should make

up time going down the grade

Further iterations were performed with the following set of input data:

1. CDA = 0.3 ft2

2. Vehicle weight = 250 lbf

3. Wind speed = 10 mph

4. Standard human power curve

80

Drag Area

Figure 46: Distance traveled as a function of CDA

From Figure 46, it is evident that the total distance traveled is dependent on the

CDA of the vehicle. Relatively small improvements in this factor lead to large

gains in distance, as one would expect from the cubic nature of aerodynamic

resistance as it relates to velocity (see Equation 2 and Equation 12).

81

Rolling Resistance

Figure 47: Distance traveled as a function of rolling resistance

Figure 47 stresses that the dependence of distance traveled on rolling resistance is

a relatively simple trend – the two are linearly dependent on each other.

82

Grade

Figure 48: Distance traveled as a function of grade

The distance traveled as a function of grade is a more simple relationship than the

aerodynamic aspects. As should be noted from Figure 48, the total distance

traveled is basically linear with respect to track grade.

83

Wind Speed

Figure 49: Distance traveled as a function of wind speed

From the Drag Area iteration section mentioned earlier, due to the dramatic

increase in aerodynamic forces when the vehicle faces a headwind, on a circuit

course, the rider should relax when headed into the wind, and make up the time

going on the backstretch with the wind. Figure 49 illustrates the relative

importance of this strategy. As the wind loading increases, the total distance

traveled decreases linearly.

84

Human Power

Figure 50: Distance traveled as a function of human power

Using the standard rider profile discussed in the Scaling Technique section, the

total possible distance for the vehicle is analyzed with respect to the rider’s

capacity as a factor of the typical rider. The most significant point is the fact that

increasing rider power has a nonlinear effect on the distance traveled. It can

therefore be said that the performance of a typical rider can benefit significantly

from design improvements. A professional athlete will not be able to perform

that much better.

85

Program Structure

The program analyzes one lap of the one-hour time trial, breaking it into a finite

number of segments.

For each segment, the following relationship is used:

[ ]ef aero rr incline accelP V F F F F Vη − + + =

Equation 11: Energy model equation

where P is the power needed to overcome the sum of the retarding forces, V is

the vehicle velocity, Faero is the force due to aerodynamic drag, Frr is the force due

to rolling resistance, Fincline is the force due to road grade, Faccel is the force

required for acceleration, and ηtrans is the transmission efficiency.

The individual forces in Equation 11 are calculated as follows:

( )2

2D hw

aero

C A V VF

ρ −=

Equation 12: Force due to aerodynamic drag

where Faero is the force due to aerodynamic drag, CD is the drag coefficient, ρ is

the density of air, A is the characteristic area, V is the vehicle velocity, and Vhw is

the wind velocity

2.5( 3.24 )rr o sF N f f V= +

Equation 13: Force due to rolling resistance

86

where Frr is the force due to rolling resistance, N is the normal force of the

vehicle, fo is the coefficient of rolling resistance (standard – a function of tire

pressure, surface, and wall flexibility), fs is the coefficient of rolling resistance

dependent on velocity, and V is the vehicle velocity [Gillespie. 1992]

sin( )inclineF W ϕ=

Equation 14: Force due to the road grade

where Fincline is the force due to the road grade, W is the weight of the vehicle, and

φ is the angle of incline

2 2

2i

accelV VF M

x−

=

Equation 15: Force required for acceleration

where Faccel is the force required for acceleration, V is the velocity, Vi is the

velocity of the previous segment, x is the distance traveled over the segment, and

M is the vehicle mass.

With the equations listed above, power requirements are generated for each finite

segment of the track as the program iterates through possible velocities. In the

end, a power profile is generated and tested such that the distance the vehicle

travels is maximized, yet the human power profile with scaling is not violated.

This process allows for optimization of specific aspects of the program as

illustrated through the previous iterations. It also can be used to point out

significant trends in the analysis.

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• Aerodynamics is the most significant force that the vehicle encounters.

Figure 51 shows that for a rider on a traditional upright bicycle, the

aerodynamic power loss is the dominant term and should be addressed in

order to go faster.

Figure 51: Power as a function of vehicle velocity for a rider on a traditional upright bicycle

Figure 52 is a similar plot to Figure 51, but it is for the same rider on the

Project Cadence vehicle. The aerodynamic power loss now does not

dominate, but rather the rolling resistance does, until around 50 ft/sec (34

mph).

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Figure 52: Power as a function of velocity for a rider on the Project Cadence vehicle

• Even a minimal fairing is an improvement over a standard upright bicycle

• The benefits of a fairing outweigh any cost of its additional weight that

the rider must overcome

• A rider will be able to travel farther if he relaxes while heading into the

wind and makes up time traveling downwind

• A rider should maintain the same trend when encountering a hill,

however in general, the degree of relaxing and catching up is not as

dramatic as when facing wind as it directly effects the aerodynamic

aspects

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Prototype

A prototype of the mechanical system (i.e., the frame, tires, wheels, drivetrain,

and other internal components) of the vehicle has already been constructed with

the assistance of professional bicycle builders [Jung. 2002-2003]. This prototype

served as a “proof of concept” to investigate the possibility of building and riding

a vehicle of the given design. The prototype also serves as a guide to make small

improvements in the final vehicle frame design.

Figure 53: Project Cadence prototype

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S e c t i o n 6

CONCLUSIONS AND FUTURE WORK

Conclusions

The design of this human powered vehicle was predominantly an endeavor in

aerodynamics. Figure 51 and Figure 52 show the extreme improvements in

aerodynamics of the Project Cadence vehicle over a standard upright bicycle.

With these improvements alone, the analysis suggests that the vehicle is capable

of covering 32 miles in one hour. To compete for the Dempsey – MacCready

Hour Record Prize, further advancements are necessary in all other aspects of the

design. Figure 52 shows that significant improvements in rolling resistance will

result in the greatest increase in performance. Advancements in aerodynamics

are also possible with more insight into the issue of protuberance drag associated

with the wheels and wheel fairings.

The argument exists that another significant area of improvement would be the

athletic ability of the rider. Figure 50 shows that a professional athlete who is

twice as powerful as the rider modeled with this design will only be able to travel

approximately three miles farther in one hour using the Project Cadence vehicle.

Therefore, it is quite possible that an average “healthy person” who has focused

their efforts on scientific improvements in design may win the Dempsey –

MacCready Hour Record Prize before a professional athlete.

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Future Work

With a vehicle fully designed, the next stages of the project would involve the

following five steps:

1. Further verification that the Psarevo fairing shape has the CDA on the

order of what was calculated

2. Construction of the complete vehicle

3. Determining the actual properties and characteristics of the complete

vehicle

4. Inputting those properties into the Energy Model to predict performance

5. Testing the vehicle on the track to see if the predictions and actual

performance are in agreement

Because of the difficulties with aerodynamic modeling and CFD calculations, the

next best option is to test at full-scale. Two wind tunnel facilities have donated

the use of their full-scale wind tunnels, NASA Langley and Modine

Manufacturing. Neither of these facilities have the equipment sensitive enough

to measure the small drag forces acting on the vehicle; however both have wind

tunnels have excellent flow visualization capacity, which would enable the

verification of the location of flow transition on the body at different velocities.

If drag-measuring equipment were to be used, it would need to be assembled and

tested for accuracy.

A full-scale fairing would need to be constructed for testing in the wind tunnels.

It is necessary to verify the actual drag of the vehicle, including the increased drag

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due to wheel protrusions. Also, the actual location of transition from laminar to

turbulent flow on the body would be necessary for a more accurate prediction of

drag using the boundary layer model.

The full-scale aerodynamic fairing would initially be built out of foam and given a

smooth finish similar to a highly sanded and polished surface. The foam model

would provide the option for making small design adjustments at the time of

testing based on wind tunnel findings. In addition, the light material would be

very responsive in the flow, enabling sensitive force measurements.

The same foam model would then serve as the master shape from which a female

mold would be constructed. With a female mold, the final composite fairing

would be constructed in two sections. In addition to the main fairing body,

wheel fairings and disk enclosures would be constructed from the same material

and finished in the same manner. The surface of the fairing would be sanded and

polished to be smooth.

With the fairing and frame, a mounting system would need to be implemented

that isolates the vibrations of the frame from the fairing. Excess road vibration, if

transmitted to the fairing, could cause premature transition of flow or separation,

both of which would cause an increase of drag [Weaver 2002].

With the vehicle fully assembled, its aerodynamic properties, rolling resistance

properties, and transmission efficiency known, a prediction of the vehicle’s

performance would be made using the Energy Model. The rider would need to

practice and train riding the fully faired vehicle. The final step would be to

perform an actual 1-hour time trial on the track to measure the distance covered.

Based on the design presented, the actual vehicle should travel no less than 32

miles in one hour, which would meet or exceed the original project goal of

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achieving a performance level of 150% of the rider on a traditional upright

bicycle.

96

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APPENDIX – MATLAB CODE

PROJECT CADENCE: HUMAN POWERED VEHICLE by Amoz Eckerson John

Documents

Transcript of PROJECT CADENCE: HUMAN POWERED VEHICLE by Amoz Eckerson John