Physics of Cycling - Ride Day by suchenfz

VIEWS: 11 PAGES: 46

• pg 1
```									Cycling Physics While Cycling
Let’s Ride!
Introduction Video Sequence
Available Here
Cycling Physics While Cycling
Goal #1
Explore Physics
• Work, Power, & Energy Dynamics.
• Angular & Linear Momentum – Balancing
• Torque Management – Gear systems
• Advanced Kinematics – Motion Analysis
Goal #2
Demonstrate Discussed Topics
• Seven hour bike ride in classroom.
• Maintain ~ 20 mph pace. (Ultimate goal = ~140 miles)
• Mandatory stretch break once per class.
• Bathroom breaks permitted!
• Additional stoppage allowed but ultimately
reduces time to reach goal.
Goal #3
Monitor Physical and Biological Progress
• The following real-time information will be
projected continuously for all to see:
1. Accumulated Mileage (miles)
2. Current Speed (miles per hour)
3. % of Max Heart Rate (based on 185 beats per minute)
4. Cadence (pedal strokes per minute)
Goal #4
• Introduce the Seminole Cyclists
• Support American Diabetes Association’s
TourdeCure Campaign
• Official 100 mile event is February 28th.
• This is my warm-up!
• 100% of today’s sponsorship will be passed to
Target Audience
Primary
• Students of Mr. Luther Davis
Physics Teacher, Lake Mary High School, Florida
Material is integrated into Physics Curriculum
• Students of Lake Mary High School
• Seminole Cyclists of Central Florida
• Fans of Cycling
• Fans of Physics
Cycling Physics
Work
Work
Work - Amount of energy required to accomplish
a physical feat
• Newton’s 1st Law implies that once in motion,
motion is maintained naturally.
• If cycling at a constant speed, why does the
rider still have to do work?
Work
• Riders battle effects of air resistance and
friction.
• If moving at a constant speed, the FORCE that
a rider provides for forward motion is exactly
equivalent to the sum of all resistances and
frictions. This includes air/bike, air/rider,
Work
• Work = Force X Distance
• Force is provided by the rider via the drive
train to the road to counteract resistance.
• Distance is the distance traveled.
• More Force or Distance means more work
done.
Power
Power
• Power - The rate at which work is accomplished
• If much work is accomplished in a short time,
much power is produced.
• If little work is accomplished in a long time,
little power is produced.
• Power = Work / Time
• Power has units of Wattage or Horsepower.
Power
• Most riders hover around 250 Watts (~0.3 hp).
• A sprinter may generate 2000 Watts (~2.5 hp)
for a few seconds.
Power
• If a rider can reduce power and still be fast,
they are efficient. One way to accomplish this
is to sit in a more aerodynamic position.
Power
• Power is the best measure of a
cyclist’s effort.
• However; it is difficult to
measure the force a rider
exerts providing forward
motion.
• Electronic meters in rear
wheels can measure power
directly via sensors. Very
expensive.
Power
Heart Rate – Another Measure of Power
• Heart Rate also indicates the power effort of a
cyclist.
• A greater rate indicates a greater effort.
• However; heart rate data is fickle; it is affected
by other factors such as stress, temperature,
and sickness.
Power
Heart Rate – A cheaper alternative
• Many sports watches offer heart
rate monitoring.
• My chest sensor measures
electrical impulses of the beating
heart.
• I use percent of maximum heart
rate to gauge my effort.
Power
Heart Rate – What percents mean to me!
• 24% = Resting Heart Rate (44 bpm for 185 bpm maximum)
• 60% = Easy…Easy workout (111 bpm)
• 70% = Easy workout (130 bpm)
• 80% = Moderate difficultly workout (148 bpm)
• 90% = Hard workout, on verge of lactic threshold (167 bpm)
• 90% - 100% = Sprinting, unable to fully recover during ride.
Power
Today’s Plan…
• Traveling nearly 140 miles, I can’t say “Let’s do
a 85% workout!”
• I plan to stay around 75%.
• I will NOT conduct sprints or intervals during
the event. I would not fully recover and my
ultimate goal would be in jeopardy.
Balance
Balance
A Stationary Bike is Unsafe
• A bike is unstable when not moving.
• It only has two contact points creating a line.
• It has no base for support.
• Consider the difference between a two and
three legged chair!
Balance
A Moving Bike is Stable
• Angular momentum keeps wheels behaving
like gyroscopes.
• Angular momentum is a property of spinning
objects.
• The bicycle wheel wants to maintain the same
plane of orientation as it spins.
Balance
• Additionally, a wheel will naturally steer itself
back under the center of gravity as a bike
begins to lean.
• This effect helps maintain bicycle balance.
Balance
Linear Momentum Effects
• Linear momentum is a result of an objects
inertia.
• As a bicycle and rider travel, they themselves
have a tendency to maintain the same travel
path.
• Manual steering helps keep wheels under the
center of gravity as well.
Balance
• Which of the two momentums am I taking
• How is it that the other is not being utilized?
• Do you think this makes it more or less
difficult to ride on this apparatus as compared
Torque
Torque
Torque – A rotational force
• Muscle force pushes pedals at a point away
from a shaft causing the shaft to rotate.
• Torque = Force X Lever Arm Distance
• Bigger Force = Bigger Torque (the pedal length is not changed)
• Torque is transferred to the rear wheel.
• The wheel then places a force on the road.
• The bike moves forward.
Torque - Gearing
• Torque is managed through a bicycle’s gearing
system using four major components:

Rear Sprockets                               Front Derailleur

Rear Derailleur                             Front Sprockets
Torque – Gearing
My Bike…
• Three sprockets up front with 52-39-30
teeth.
• 10 sprockets in rear with 12-13-14-15-16-
17-19-21-23-25 teeth.
• Combination yields 30 gear ratios.
• Derailleurs move the chain from
sprocket to sprocket.
• Derailleurs controlled by hand shifters.
Torque - Gearing
• Adjusting gears can control how much force
one needs to apply to pedals for motion.
• At one extreme, one pedal rotation = 4.33
wheel rotations (high gear).
This produces great speed but requires great force. A cyclist may use
this when going with wind or downhill.

• At the other extreme, one pedal rotation =
1.2 wheel rotations (low gear).
This produces small speed but requires small force. A cyclist may
use this when going against wind or uphill.
Gear Ratio & Data Chart
Distance                                                          Distance
Traveled       Pedal                                              Traveled      Pedal
S hifting     Used      per Pedal    Rotations                    Shifting      Used      per Pedal   Rotations
P at tern   Sprockets   Rotation      per Mile   Gear Ratio       P at tern   Sprockets   Rotation     per Mile   Gear Ratio
1          30x25      8' 8.05"      608.9      1 : 1.20           16        30x13      16' 8.10"     316.7      1 :2.31
2          30x23      9' 5.10"      560.2      1 : 1.30           17        39x16      17' 7.35"     299.8      1 :2.44
3          30x21     10' 3.87"      511.5      1 : 1.43           18        52x21      17'10.71"     295.1      1 : 2.48
4          39x25     11' 3.26"      468.4      1 :1.56            19        30x12      18' 0.77"     292.3      1 : 2.50
5          30x19     11' 4.91"      462.8      1 : 1.58           20        39x15      18' 9.44"     281.1      1 : 2.60
6          39x23     12' 3.03"      430.9      1 :1.70            21        52x19      19' 9.31"     267.0      1 : 2.74
7          30x17     12' 9.01"      414.1      1 : 1.76           22        39x14      20' 1.54"     262.3      1 : 2.79
8          39x21     13' 5.03"      393.5      1 : 1.86           23        39x13      21' 8.12"     243.6      1 : 3.00
9          30x16     13' 6.58"      389.7      1 : 1.88           24        52x17      22' 1.22"     238.9      1 : 3.06
10         30x15     14' 5.42"      365.4      1 :2.00            25        52x16      23' 5.80"     224.8      1 : 3.25
11         39x19     14' 9.98"      356.0      1 : 2.05           26        39x12      23' 5.80"     224.8      1 : 3.25
12         52x25     15' 0.35"      351.3      1 : 2.08           27        52x15      25' 0.59"     210.8      1 : 3.47
13         30x14     15' 5.80"      341.0      1 : 2.14           28        52x14      26'10.06"     196.7      1 : 3.71
14         52x23     16' 4.04"      323.2      1 : 2.26           29        52x13      28'10.83"     182.7      1 : 4.00
15         39x17     16' 6.92"      318.5      1 : 2.29           30        52x12      31' 3.73"     168.6      1 : 4.33

Smallest Front                  Medium Front              Largest Front
Sprocket                        Sprocket                  Sprocket
Torque - Gearing
• Cyclist like to maintain a certain effort and
pedal rate. I personally like to stay around 90
rpm.
• Using the gearing system I can maintain my
comfort levels over the various terrain a wind
speed changes.
• In essence, I keep Torque the same, always
finding a compromise between Force and
Distance (T = F X d).
Kinetic Energy
Kinetic Energy
Kinetic Energy is Energy of Motion
• KE = ½ mv2
• Changes velocity, result in KE changes.
• A doubling of speed (ex. 15 mph to 30 mph)
produces four times as much kinetic energy.
• Air resistance also has a square effect on
force.
• Result: Cyclist do four times as much work
every time they double their speed!
Kinematics
Kinematics
Analysis of Motion
• For long distances where constant motion is
prevalent, d=vt is sufficient.
• For sprints, accelerations and braking, typical
kinematic accelerations can be applied:
vf = vi + at
d = vit + ½ at2
d = ½ (vf + vi)t
What Do I Think About When Riding?
• On many rides, cyclists set a goal average
speed. It can be hard to achieve,
especially when going with and against
the wind at different times on the same
ride.
• Scenario… I want to cycle 80 miles and
average 20 mph. I go 40 miles to New
Smyrna from Longwood against the wind
and only average 17 mph.
• How fast must I cycle back?
• Answer: Some may think 23 mph…
• Not the case. The 17 mph half outweighs the
effect of the 23 mph because it takes more
time than the 23 mph half. The effects are not
equal, therefore they would average to
something under 20mph.
• I must cycle faster than 23.
• How much?
• Curiosity got the best of me and I developed
the following equation:

• Where vBack = required velocity coming back to
get a desired average velocity (vAvg) after going
out with velocity (vOut).
• For my scenario, vBack = 24.3, not 23 mph.
• Equation works for hills also!
Top Row = Desired Average Velocity (mph)
16      16.5   17 17.5       18     18.5   19     19.5    20     20.5   21     21.5    22     22.5   23
First Column = Uphill or “Out” Velocity (mph)

8    X       X      X      X      X      X      X      X      X       X      X      X      X       X      X
9   72.0    99.0    X      X      X      X      X      X      X       X      X      X      X       X      X
10   40.0    47.1   56.7   70.0   90.0   123.3 190.0 390.0     X       X      X      X      X       X      X
11   29.3    33.0   37.4   42.8   49.5   58.1   69.7   85.8   110.0   150.3 231.0 473.0     X       X      X
12   24.0    26.4   29.1   32.3   36.0   40.4   45.6   52.0   60.0    70.3   84.0 103.2    132.0   180.0 276.0
13   20.8    22.6   24.6   26.8   29.3   32.1   35.3   39.0   43.3    48.5   54.6   62.1   71.5    83.6   99.7
14   18.7    20.1   21.6   23.3   25.2   27.3   29.6   32.1   35.0    38.3   42.0   46.3   51.3    57.3   64.4
15   17.1    18.3   19.6   21.0   22.5   24.1   25.9   27.9   30.0    32.4   35.0   37.9   41.3    45.0   49.3
16   16.0    17.0   18.1   19.3   20.6   21.9   23.4   25.0   26.7    28.5   30.5   32.8   35.2    37.9   40.9
17   15.1    16.0   17.0   18.0   19.1   20.3   21.5   22.9   24.3    25.8   27.5   29.2   31.2    33.3   35.5
18   14.4    15.2   16.1   17.0   18.0   19.0   20.1   21.3   22.5    23.8   25.2   26.7   28.3    30.0   31.8
19   13.8    14.6   15.4   16.2   17.1   18.0   19.0   20.0   21.1    22.3   23.5   24.8   26.1    27.6   29.1
20   13.3    14.0   14.8   15.6   16.4   17.2   18.1   19.0   20.0    21.0   22.1   23.2   24.4    25.7   27.1
21   12.9    13.6   14.3   15.0   15.8   16.5   17.3   18.2   19.1    20.0   21.0   22.0   23.1    24.2   25.4
22   12.6    13.2   13.9   14.5   15.2   16.0   16.7   17.5   18.3    19.2   20.1   21.0   22.0    23.0   24.1
23   12.3    12.9   13.5   14.1   14.8   15.5   16.2   16.9   17.7    18.5   19.3   20.2   21.1    22.0   23.0

Chart summarizes results of the equation.
Intersections show required downhill or “back” velocities.
The blue intersection is from the New Smyrna example.
X indicates – Impossible!
Cycling Physics
• Thank you for your attention.
• I wish to address any further questions at this
time.

```
To top