Physics of Cycling - Ride Day by suchenfz

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									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
  ADA for the February event.
             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
Additional
• 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,
  tires/road, chain/sprockets, bearings, etc.
                    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
More about Angular Momentum Effects
• 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
  advantage of today?
• 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
  to the road?
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
  vf2 = vi2 + 2ad
What Do I Think About When Riding?
  Yep, Advanced Kinematics
• 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?
      Advanced Kinematics
• 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?
      Advanced Kinematics
• 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!
                                                            Advanced Kinematics
                                                                           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.

								
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