Cycling Physics While Cycling

Let’s Ride!Introduction Video Sequence

Available Here

Cycling Physics While Cycling

Goal #1Explore 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 #3Monitor 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, FloridaMaterial is integrated into Physics Curriculum

• Students of Lake Mary High SchoolAdditional• Seminole Cyclists of Central Florida• Fans of Cycling• Fans of Physics

Cycling Physics

Work

WorkWork - 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.

PowerHeart 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.

PowerHeart 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.

PowerToday’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

BalanceA 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!

BalanceA 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.

BalanceMore 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.

BalanceLinear 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

TorqueTorque – 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 – GearingMy 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 ChartShifting Pattern

Used Sprockets

Distance Traveled per Pedal Rotation

Pedal Rotations per Mile Gear Ratio

1 30x25 8' 8.05" 608.9 1 : 1.202 30x23 9' 5.10" 560.2 1 : 1.303 30x21 10' 3.87" 511.5 1 : 1.434 39x25 11' 3.26" 468.4 1 :1.565 30x19 11' 4.91" 462.8 1 : 1.586 39x23 12' 3.03" 430.9 1 :1.707 30x17 12' 9.01" 414.1 1 : 1.768 39x21 13' 5.03" 393.5 1 : 1.869 30x16 13' 6.58" 389.7 1 : 1.8810 30x15 14' 5.42" 365.4 1 :2.0011 39x19 14' 9.98" 356.0 1 : 2.0512 52x25 15' 0.35" 351.3 1 : 2.0813 30x14 15' 5.80" 341.0 1 : 2.1414 52x23 16' 4.04" 323.2 1 : 2.2615 39x17 16' 6.92" 318.5 1 : 2.29

Shifting Pattern

Used Sprockets

Distance Traveled per Pedal Rotation

Pedal Rotations per Mile Gear Ratio

16 30x13 16' 8.10" 316.7 1 :2.3117 39x16 17' 7.35" 299.8 1 :2.44

18 52x21 17'10.71" 295.1 1 : 2.4819 30x12 18' 0.77" 292.3 1 : 2.5020 39x15 18' 9.44" 281.1 1 : 2.6021 52x19 19' 9.31" 267.0 1 : 2.7422 39x14 20' 1.54" 262.3 1 : 2.7923 39x13 21' 8.12" 243.6 1 : 3.0024 52x17 22' 1.22" 238.9 1 : 3.0625 52x16 23' 5.80" 224.8 1 : 3.25

26 39x12 23' 5.80" 224.8 1 : 3.2527 52x15 25' 0.59" 210.8 1 : 3.4728 52x14 26'10.06" 196.7 1 : 3.7129 52x13 28'10.83" 182.7 1 : 4.0030 52x12 31' 3.73" 168.6 1 : 4.33

Largest Front Sprocket

Smallest Front Sprocket

Medium Front 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 EnergyKinetic 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

KinematicsAnalysis 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 = vi

2 + 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!

AvgOut

OutAvgBack vv

vvv

2

Advanced Kinematics

16 16.5 17 17.5 18 18.5 19 19.5 20 20.5 21 21.5 22 22.5 238 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!

Firs

t Col

umn

= U

phill

or

“Out

” V

eloc

ity (

mph

)

Top Row = Desired Average Velocity (mph)

Cycling Physics• Thank you for your attention. • I wish to address any further questions at this

time.