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 Associations Tour de Cure Campaign Official 100 mile event is February 28 th. This is my warm-up! 100% of todays 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
Work - Amount of energy required to accomplish a physical feat Newtons 1 st 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 - 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 cyclists 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 Todays Plan… Traveling nearly 140 miles, I cant say Lets 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.
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 – 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 bicycles gearing system using four major components: Rear SprocketsFront Derailleur Rear DerailleurFront 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.
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 is Energy of Motion KE = ½ mv 2 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!
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: v f = v i + at d = v i t + ½ at 2 d = ½ (v f + v i )t v f 2 = v i 2 + 2ad
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 v Back = required velocity coming back to get a desired average velocity (v Avg ) after going out with velocity (v Out ). For my scenario, v Back = 24.3, not 23 mph. Equation works for hills also!
Advanced Kinematics 1616.51717.51818.51919.52020.52121.52222.523 8 XXXXXXXXXXXXXXX 9 72.099.0XXXXXXXXXXXXX 10 40.047.156.770.090.0123.3190.0390.0XXXXXXX 11 29.333.037.442.849.558.169.785.8110.0150.3231.0473.0XXX 12 24.026.429.132.336.040.445.652.060.070.384.0103.2132.0180.0276.0 13 20.822.624.626.829.332.135.339.043.348.554.662.171.583.699.7 14 18.720.121.623.325.227.329.632.135.038.342.046.351.357.364.4 15 17.118.319.621.022.524.125.927.930.032.435.037.941.345.049.3 16 16.017.018.119.320.621.923.425.026.728.530.532.835.237.940.9 17 15.116.017.018.019.120.321.522.924.325.827.522.214.171.1245.5 18 14.415.216.117.018.019.020.121.322.523.825.226.728.330.031.8 19 13.814.615.416.217.118.019.020.021.122.323.524.826.127.629.1 20 13.314.014.815.616.417.218.119.020.021.022.123.224.425.727.1 21 12.913.614.315.015.816.517.318.219.120.021.022.023.124.225.4 22 12.613.213.914.515.216.016.717.518.319.220.121.022.023.024.1 23 12.312.913.514.114.815.516.216.917.718.519.320.221.122.023.0 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! First Column = Uphill or Out Velocity (mph) Top Row = Desired Average Velocity (mph)
Cycling Physics Thank you for your attention. I wish to address any further questions at this time.