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Land Wind Racer Design
RideWy
University of Wyoming
College of Engineering and Applied Sciences
EPSCoR Undergraduate Research Day
April 21, 2012
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RideWy Team
Mechanical Engineering
• Austin Rykhus – Frame Design
and construction
• Lee Mitchell – Brake Design
Energy Systems Engineering
• Nick James –Stability and
Steering Design
• Shyla Allen – Sail Design
Sponsors
• Z4 Energy
• Georgia Gayle
• Kevin Luke
Advisors
• Dr. Naughton
• Dr. Garnich
• Mr. Morton
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Celebration of Wind
Race Rules
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Wind powered
3 to 84 wheels, 5” or larger
All human crew, or as close as possible
Equipped with braking & steering
Assume liability for themselves & crew
No commercial vehicles
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Celebration of Wind
Race Rules
• Carry 1 person over course
• Height < 13.5 ft
• No chewing tobacco if the wind >15 knots
(to avoid splashing the spectators)
• Points deducted for:
Celebration of Wind
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Destroying spectators
Biting
Kicking
Striking
Gouging
Race Day
April 28, 2012
Rawlins, Wyoming
• BRIBES will be taken into consideration
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Land Wind Racer Design
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Overview
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Design Specifications
Lessons Learned
Design Approach
Modeling
Compliance Testing
Alterations
Finished Product
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Design Specifications
• Z4 Specifications
• ≤ 80 lbf weight
• 4 ft x 6 ft footprint
• “WIN the RACE”
• RideWy Specifications
• 13 mph average tailwind
• 40 mph maximum
tailwind
• 1.2 minimum FOS
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Lessons Learned
User Interface
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Rider capabilities
Steering
Braking
Sail Rigging
Sitting position
Frame
• Weight and transport
• Sail design
Head Clearance
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Design Approach
• 3 vs. 4 wheels
• 3 wheel inverted tricycle design
• Lightweight, stable, and simple
• Sail
• Spinnaker sail – tailwind application
• Braking – front vs. rear
• Dual front brakes – majority of brake force
• Steering
• Rear steering – simplicity
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Modeling – The Sail
• Created from a pressure gradient – Bernoulli’s Principle
•
1
2
L = ρ𝑉𝐴 2 AS CL
1
2
D = ρ𝑉𝐴 2 AS CD
Variable
Definition
VS
Velocity of Racer
VT
Wind Velocity
VA
Apparent Wind
• Minimum β angle = More advantageous
V
VST
• Total Propulsion Force:
•
VA
Implemented in other modeling
•
V
VT
S
β
VS/VT =3
𝐹𝑇 = 0.00119 × 𝐶𝑇 × AS × 𝑉𝐴 2
•
𝐶𝑇 =
𝐶𝐿 2 + 𝐶𝐷 2
• β = 65 °, 𝑉𝑇 = 10 mph – Propulsion Force = 25 lbf
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Modeling – The Sail
• Dynamic Modeling
• Solution relative to time (t) , distance (s), and velocity
(v)
• Differential Equations with MATLab
Variables:
• 𝑌1 = 𝑠
• 𝑌2 = 𝑣
Derivatives:
• 𝐹1 =
• 𝐹2 =
𝑑𝑠
= 𝑣 = 𝑌2
𝑑𝑡
𝑑𝑣
𝐹
=
𝑎
=
𝑑𝑡
𝑚
Variable
CT
AS
VA
Definition
Lift and Drag Coefficient
Wind Velocity
Apparent Wind
Recall:
𝐹 = 0.00119 × 𝐶𝑇 × AS × 𝑉𝐴 2
• ½ mile, β = 65 °, 𝑉𝑇 = 7 mph, Time = 3 minutes
• Maximum Velocity = 7 mph
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Modeling – Braking System
• Front disc brakes with foot pedal
• Sum the horizontal forces about the racer’s front wheel
𝑀 = 𝐹𝑓 = 𝐹𝑛 µ
• Sum the moments about the front axle for vertical forces
𝐹𝑓 𝑅𝑤ℎ𝑒𝑒𝑙 = (𝑚𝑟𝑖𝑑𝑒𝑟 𝑔)𝐿𝑟𝑖𝑑𝑒𝑟 + (𝑚𝑣 𝑔)𝐿𝑐𝑔 + (𝑚𝑣 𝑔)ℎ𝑐𝑔 + 𝐹𝑤𝑖𝑛𝑑 ℎ𝑤𝑖𝑛𝑑
Variable
Ff
Fn
Fb
M
cg
Definition
Friction Force
Normal force
Brake Force
Brake Moment
Center of Gravity
rb
Brake Disc Radius
hwind
Height of Wind force
µ
Coefficient of Friction
Cg
M
wind
rb
Fn,fw
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Modeling – Braking System
• Applied braking force
𝐹𝑓 𝑅𝑤ℎ𝑒𝑒𝑙 = 𝐼𝛼 + 𝐹𝑏 𝑟𝑏 ≈ 𝐹𝑏 𝑟𝑏
• Stopping distance
• Sail dropped, not accelerating forward
𝑉𝑠2
𝑉𝑠2
𝑆𝐷 =
=
𝐹
2𝑎
2(𝑚𝑏 )
𝑣
• Racer velocity = 20 mph, µ = 0.65
• Fb = 98 lbf
• SD = 7.5 ft
Variable
Ff
Fb
mv
Definition
Friction Force
Brake Force
Mass of Racer
rb
Brake Disc Radius
I
Moment of Inertia
α
Angular Acceleration
Vs
Velocity of Racer
SD
Stopping Distance
μ
Coefficient Of Friction
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Modeling – Stability
• Modeled using a worst case scenario
• Side Stability
Σ 𝑀𝑜𝑚𝑒𝑛𝑡𝑠 = 𝑚𝑔 𝐿 − 𝐿𝑐𝑔 sin 𝑡𝑎𝑛−1
𝑤
ℎ𝐹𝑡 𝑠𝑖𝑛 sin 𝜃𝑠 − 𝑡𝑎𝑛−1
2𝐿
𝑤
2𝐿
−
• Frontal Stability
Σ 𝑀𝑜𝑚𝑒𝑛𝑡𝑠 = 𝑚𝑔𝐿𝑐𝑔 − ℎ𝐹𝑡 𝑐𝑜𝑠𝜃𝑠 − 𝑅𝐹𝑊 𝐹𝑏
Variable
LCG
Fb
Ft
h
Ѳs
Definition
Distance to center of gravity
Brake force
Driving force from sail
Height of point force of sail
Angle of Ft
Cg
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Modeling –Steering
• Similar to bicycle steering
• Steering torque arm (nT) effected by
• Caster angle (Ѳc)
• Wheel Radius (RRW)
• Fork Offset (Of)
𝑛 𝑇 = 𝑅𝑅𝑊 𝑠𝑖𝑛𝜃𝑐 − 𝑂𝑓
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Modeling – Steering
• Centrifugal force (FC) balanced by
• FY1, FY2 and FY3 at contact points
𝐹𝑦3 = 1 −
𝐿−𝐿𝑐𝑔 3𝐹𝑐
𝐿
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Variable
VT
RT
m
Definition
Tangential velocity
Turning radius
Total mass
• Restoring Moment
𝑀𝑍 = (𝑅𝑅𝑊 𝑠𝑖𝑛𝜃𝑐 − 𝑂𝑓 ) 1 −
•
𝐿−𝐿𝑐𝑔 3𝑚𝑉𝑇2
𝐿
4𝑅𝑇
Of = 1in and θc = 15°
Velocity (mph)
Turning Radius (ft)
Restoring Torque (ft-lbf)
10
25
20
50
4.2 ± 0.6
11± 1.3
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Modeling
Lateral Wheel Forces
• Front wheel camber
• Reduce lateral loads
• Total lateral load
Variable
FY2
NFW
RFW
θcam
Definition
Cornering force at front wheel
Normal force at front wheel
Front wheel radius
Camber angle
∑𝐹𝐹𝑊 = 𝑁𝐹𝑊 cos 90 − 𝜃𝑐𝑎𝑚 − 𝐹𝑌2 cos𝜃𝑐𝑎𝑚
𝐹𝑌2 =
𝐿−𝐿𝑐𝑔 3𝑚𝑉𝑇2
𝐿
4𝑅𝑇
• Camber – 10°
• Reduces lateral loads by 25%
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Frame Analysis
• Compare and Validate each model
• Beam analysis
• Finite Element Analysis
in SolidWorks
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T –Frame Analysis
m1
m2
m3
Rider mass
Mast mass
Front axle mass
Ry_1
Reaction force in the y-direction
Ry-2
Reaction force in the y-direction
W1 , W2 Frame distributed load
X1
Distance to mass 1
X2
Distance to the mast
M
Moment about the mast in the ydirection
Not accounting for the beam slope or
deformation at this point
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T –Frame Analysis
• MATLAB T Design
• m1=140 lbf
• m2=13 lbf
• M=Ft*5.7 ft
• Ft=20 lbf
• Diagrams
• Shear
• Moment
• Results
• σ’ =8300 psi
• FOS=4.9
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Frame Analysis
• Stress analysis on frame using SolidWorks Simulation
• FEA T Design
• m1=140 lbf
• m2=13 lbf
• M=Ft*5.7 ft
• Ft=20 lbf
• Results
• σ’ =7700 psi
• FOS=5.4
• Beam Analysis and FEA was performed on the Delta Design
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Comparing Frame Analysis
• T – Frame
• Weight: 28 lbf
• 1.6-1.9 FOS
• Delta Frame
• Weight: 31 lbf
• 1.8-2.0 FOS
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Fabrication
• Construction began February 22,
2012
• Components fabricated
• Frame
• Running gear
• Wheels & brakes
• Modified bike components
• Sail – Club 420 modified
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Compliance Testing
Sail Testing
• Sail mounted to support post
• Sail force using force dynamometer
• Results
• Wind = 7.5 mph, 20 lbf
Frame Testing
• Frame fixed to ground
• Forces applied & deflection recorded
• Results
• 150 lbf rider, 70 lbf wind – 0.05 inches
• Linear behavior – elastic strain region
• Theoretical results
• 150 lbf rider, 70 lbf wind – 0.03 inches
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Compliance Testing
Brake Testing
• 150 lbf rider
• Force dynamometer pulled to
measure brake resistance
• Results
• Modeled force = 98 lbf
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Tested force = 53 lbf
Stopping Distance = 10.5 ft
Tipping Testing
• Rear wheel fixed, racer rotation
about right front wheel
• 150 lbf rider
• Dynamometer pulled on mast until
tipped
Results – Side load
• Modeled force = 35 lbf
• Tested force = 32 lbf
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Alterations Made After Testing
• The foot rest and braking pedal
• Ergonomic issues
• Sail control
• Add line guides to front axle
• Steering geometry
• Improve restoring force
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Finished Product
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Sponsors
• Z4 Energy
• Sponsorship & Funding
• North Sails & Sail Newport
• Spinnaker Sail
• Mckims’s Upholstery
• Seat Upholstery
• Department of Family and
Consumer Sciences
• Dr. Sonya Meyer
• Dr. Donna Brown
• Sail Alterations
• Moonbuggy Team
• Wheels and Brakes
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Special Thanks
Faculty & Shop Technicians
Dr. Erikson
Mr. Allen
Mr. Schilt
Mr. Dauer
Mr. Morton
Dr. Naughton
Dr. Garnich
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Questions!
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