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 Basic Terminology (fill in the details as a class) Work: Energy: Power: Force: Torque: Work/Energy Work is done on an object if a nonzero component of the force exists in the direction of motion. The magnitude of the work is W= Fs s where Fs is the component of force in the direction of s and s is the distance moved Units of Work: lb-ft British Joule (N-m) mks erg (dyne-cm) cgs other forms: calorie = 4.186 J = .239 W- sec, (note the number of calories listed on your cereal box are really in units of kilocalories) Kw-hr BTU = 778 ft-lb=252 calories Power is the rate of doing work P=work done/time taken = F s/t Also = F * velocity = Torque * rotational speed (radians/sec) Units: HP = 550 lb-ft/sec Watt (Joule/sec) HP = 746 Watts

Newton’s Second Law SF = ma = m dv/dt F4 F1 m F2 F3 a A Rigid Body C.G.

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

Free Body Diagram of Motive Force 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. used by permission of Human Kinetics Books, ©1986, all rights reserved 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.

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 refers to the orientation of the pedal with respect to a reference frame fixed in the cycle (vertical to level ground). used by permission of Human Kinetics Books, ©1986, all rights reserved

Effective and Unused Force Fe is effective force which produces motive torque. Fu º Fr-Fe = unused force. Fr In your journal (for extra credit), show that: Fe = Fr sin (q1 + q2 -q3) Fp = Fr cos (q1 + q2 -q3)

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

Combined Forces of Both Legs used by permission of Human Kinetics Books, ©1986, all rights reserved 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)

Are Toe-Clips Worth the Trouble?

Pedaling Speed Optimum speed for most people is 55-85 rpm. MOST EFFICIENT PEDALLING 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) used by permission of Human Kinetics Books, ©1986, all rights reserved

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 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 (ref 3. pg 112)

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)

Some Empirical Data 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. (ref 3, pg 126) used by permission of Human Kinetics Books, ©1986, all rights reserved

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 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 Conservation of Energy, for any system: Energyin = Energyout + Change in Stored Energy Energy input Internal Energy of System Energy Output SYSTEM