Published on February 5, 2008
Biomechanics of Cycling: Biomechanics of Cycling 1. Why do we shift gears on a bicycle? 2. Are toe-clips worth the trouble? 3. What determines how fast our bike goes for a given power input? Cycling Bio-Mechanics: Cycling Bio-Mechanics Basic Terminology (fill in the details as a class) Work: Energy: Power: Force: Torque: Newton’s Second Law: Newton’s Second Law SF = ma = m dv/dt C.G. A Rigid Body Forces Acting on a Bicycle at Rest: Forces Acting on a Bicycle at Rest used by permission of Human Kinetics Books, ©1986, all rights reserved Forces Acting on a Moving Bicycle: used by permission of Human Kinetics Books, ©1986, all rights reserved Forces Acting on a Moving Bicycle Free Body Diagram of Motive Force: Free Body Diagram of Motive Force Working with your group, derive the relationship between F1 and F4 as a function of L1-L4. Next, derive the relationship between V1 and V4. used by permission of Human Kinetics Books, ©1986, all rights reserved Purpose of bike transmission is to convert the high force, low velocity at the pedal to a higher velocity (and necessarily lower force) at the wheel. Changing Force versus Speed: Changing Force versus Speed Using the relationships you derived, complete the table from Session 1. Does this agree with had previously? Why or why not? Is the relationship between F1 and F4 constant? Ankling : Ankling used by permission of Human Kinetics Books, ©1986, all rights reserved Ankling refers to the orientation of the pedal with respect to a reference frame fixed in the cycle (vertical to level ground). Effective and Unused Force: Effective and Unused Force In your journal, show that: Fe = Fr sin (q1 + q2 -q3) Fp = Fr cos (q1 + q2 -q3) Fr Fe is effective force which produces motive torque. Fu º Fr-Fe = unused force. Pedal Forces - Clock Diagram: Pedal Forces - Clock Diagram A clock diagram showing the total foot force for a group of elite pursuit riders using toe clips, at 100 rpm and 400 W. Note the orientation of the force vector during the first half of the revolution and the absence of pull-up forces in the second half. How Pedal Forces Vary over Time: How Pedal Forces Vary over Time Combined Forces of Both Legs: Combined Forces of Both Legs A plot of the horizontal force between the rear wheel and the road due to each leg (total force is shown as the bold solid line). Note that this force is not constant, due to the fact that the force applied at the pedal is only partly effective. (ref 3, pg 107) used by permission of Human Kinetics Books, ©1986, all rights reserved Are Toe-Clips Worth the Trouble?: Are Toe-Clips Worth the Trouble? Pedaling Speed: Pedaling Speed Optimum speed for most people is 55-85 rpm. This yields the most useful power output for a given caloric usage. (ref 3, pg 79) MOST EFFICIENT PEDALLING SPEED used by permission of Human Kinetics Books, ©1986, all rights reserved Human Power Output: Human Power Output Most adults can deliver 0.1 HP (75 watts) continuously while pedaling which results in a typical speed of 12 mph. Well-trained cyclists can produce 0.25 to 0.40 HP continuously resulting in 20 to 24 mph. World champion cyclists can produce almost 0.6 HP (450 watts) for periods of one hour or more - resulting in 27 to 30 mph. Why do the champion cyclists go only about twice as fast if they can produce nearly 6 times as much power? Human Power Output: (ref 3. pg 112) Human Power Output The maximum power output that can be sustained for various time durations for champion cyclists. Average power output over long distances is less than 400 W. used by permission of Human Kinetics Books, ©1986, all rights reserved The Forces Working Against Us: The Forces Working Against Us Drag Force due to air resistance: Fdrag =CdragV2 A Cdrag = drag coefficient (a function of the shape of the body and the density of the fluid) A = frontal area of body V = velocity Since: Power = Force x Velocity to double your speed requires 8 times as much power just to overcome air drag (since power ~ velocity3) SomeEmpiricalData: Some Empirical Data (ref 3, pg 126) Drag force on a cycle versus speed showing the effect of rider position. The wind tunnel measurements are less than the coast-down data because the wheels were stationary and rolling resistance was absent. used by permission of Human Kinetics Books, ©1986, all rights reserved Other Forces Working Against Us: Other Forces Working Against Us Rolling Resistance Frr=Crr x Weight Typical values for Crr: knobby tires 0.014 road racing tires 0.004 Mechanical Friction (bearings, gear train) absorbs typically only 3-5% of power input if well maintained Other Energy Absorbers: Other Energy Absorbers Hills (energy storage or potential energy) Change in Potential Energy = Weight x Change in elevation (h) h Here, the rider has stored up energy equal to the combined weight of rider and bike times the vertical distance climbed. The First Law of Thermodynamics: The First Law of Thermodynamics Conservation of Energy, for any system: Energyin = Energyout + Change in Stored Energy SYSTEM Energy input Energy Output Internal Energy of System Now Put it All Together:: Now Put it All Together: Velocity = fcn [ power input (pedal rpm, pedal force), road slope, rider weight, bike weight, frontal area, rider position, gear ratio, tire type and inflation, maintenance ...] Your task: (as homework, due Feb. 11, use computer (spreadsheet program like EXCEL) for analysis and presentation of results). You can work with your bicycle dissection partner if you want. 1. Using first law of thermodynamics, derive the relation between the relevant factors to calculate V (bike velocity). Clearly state all assumptions. 2. Generate a graph relating speed to hill grade (from 0% to 20%) for riders weighing 140, 160, 180, and 200 lbs who are exerting a continuous power of 0.1 HP.