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    Cycling Bio-Mechanics

    n Basic Terminology (fill in the details as a class) Work

    Energy

    Power

    Force

    Torque

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    Things Ive always

    wondered about1. Why do we shift gears on a bicycle?

    2. What determines how fast our bike goes for a

    given power input?3. Are toeclips worth the trouble?

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    Newtons Second Law

    F = ma = m dv/dt

    F1

    F2

    F3

    F4

    m

    aC.G. A Rigid Body

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    External Forces acting on BikeRIDER WEIGHT WIND RESISTANCE

    HANDLEBAR FORCE

    BIKE WEIGHT

    GROUND REACTION FORCES

    PEDALFORCE

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    Force Transmission

    Purpose of bike transmissionis to convert the high force, low

    velocity at the pedal to ahigher velocity (and necessarilylower force) at the wheel. Thepower at pedal (F1 x V1) equalsthe power at the wheel (F4 x V4)(assuming no friction losses)

    L1

    L2

    L3F1

    F2F3=F2

    F4

    L4

    F4 = F1 x ?

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    Pedal Forces

    (ref 3, pg 105)

    A clock diagram showing thetotal foot force for a group ofelite pursuit riders using toe

    clips, at 100 rpm and 400 W.Note the orientation of the forcevector during the first half of therevolution and the absence ofpull-up forces in the secondhalf.

    used by permission of Human Kinetics Books,1986, all rights reserved

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    Pedal Force Components

    Fr = Total Foot Force

    Fe=Effective Force

    (causes useful Torque)

    The total foot force can be resolvedinto vector components

    PEDAL

    CRANK

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    Effective Pedal Force

    (ref 3, pg 106)

    EFFECTIVE FORCE

    RESULTANT FORCE

    UNUSED FORCE

    NEGATIVE EFFECTIVE FORCE

    CRANK ANGLE (Degrees)

    FORCE(N)

    0 180 360

    used by permission of Human Kinetics Books,1986, all rights reserved

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    HorizontalForce between

    Rear Wheel andRoad

    (ref 3, pg 107)

    A plot of the horizontal force between the rear wheel and the road,due to each leg. The total force is shown as the bold solid line.Note that this force is not constant, due to the fact that the forceapplied at the pedal is only partly effective.

    used by permission of Human Kinetics Books,1986, all rights reserved

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    Pedal Speed

    Optimum speed for mostpeople is 55-85 rpm.This yields the mostuseful power output for a

    given caloric usage (ref 3, pg 79)

    MOST EFFICIENTPEDALLING SPEED

    used by permission of Human Kinetics Books,1986, all rights reserved

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    Human Power Output

    n Most adults can deliver .1 HP (75 watts)continuously while pedaling which results in atypical speed of 12 mph

    n Well-trained cyclists can produce .25 to.40 HPcontinuously resulting in 20 to 24 mph

    n World champion cyclists can produce almost .6HP (450 watts) for periods of one hour or more -resulting in 27 to 30 mph

    Why do the champion cyclists only goabout twice as fast if they can producenearly 6 times as much power?

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    (ref 3. pg 112)

    Human Power Output

    The maximum power output that can be sustained forvarious time durations for champion cyclists. Averagepower output over long distances is less than 400 W.

    used by permission of Human Kinetics Books,1986, all rights reserved

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    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 thedensity of the fluid)

    A = frontal area of body

    V = velocity

    and since: Power = Force x Velocity

    This means that, to double your speed requires 8 times

    as much power just to overcome air drag (sincepower ~ velocity3)

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    Some Empirical

    Data

    (ref 3, pg 126)

    Drag force on a cycle versus speed

    showing the effect of rider position. Thewind tunnel measurements are lessthan the coast-down data because thewheels were stationary and rollingresistance was absent.

    used by permission of Human Kinetics Books,1986, all rights reserved

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    Forces - continued

    n Rolling Resistance Frr=Crr x Weighttypical values for Crr:

    knobby tires .014

    road racing tires .004

    n Mechanical Friction (bearings, gear train)absorbs typically only 3-5% of power input if well maintained

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    Other Energy Absorbers

    n Hills (energy storage or potential energy)Change in Potential Energy = Weight x Change in elevation (Dh)

    Dh Here, the rider has stored up

    energy equal to the combinedweight of rider and bike timesthe vertical distance climbed.

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    The First Law of

    Thermodynamicsn Conservation of Energy, for any system:

    Energyin = Energyout +Change in Stored Energy

    SYSTEM

    Energy input

    Energy Output

    Internal Energyof System

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    Now Put it All Together:

    Velocity = f[ power input (pedal rpm, pedal force), road slope,rider weight, bike weight, frontal area, rider position, gearratio, tire type and inflation, maintenance ...]

    Your task:(as homework, due in one week, use computer(spreadsheet program like EXCEL) for analysis and presentation ofresults)

    1. Using first law of thermodynamics, derive the relation between therelevant factors to calculate V (bike velocity). Clearly state allassumptions.

    2. Generate a graph relating speed to hill grade (from 0% to 20%) for

    riders weighing 120, 140, 160, 180 and 200 pounds who areexerting a continuous power of 0.1 HP.

    3. Determine the terminal velocity of the 160 lb rider coasting goingdown a 10% grade.