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1 ME240/105S: Product Dissection 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?

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2 ME240/105S: Product Dissection Cycling Bio-Mechanics n Basic Terminology (fill in the details as a class) –Work: –Energy: –Power: –Force: –Torque:

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3 ME240/105S: Product Dissection Newton’s Second Law F = ma = m dv/dt F1 F2 F3 F4 m a C.G. A Rigid Body

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4 ME240/105S: Product Dissection Forces Acting on a Bicycle at Rest used by permission of Human Kinetics Books, ©1986, all rights reserved

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5 ME240/105S: Product Dissection used by permission of Human Kinetics Books, ©1986, all rights reserved Forces Acting on a Moving Bicycle

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6 ME240/105S: Product Dissection Free Body Diagram of Motive Force n Working with your group, derive the relationship between F1 and F4 as a function of L1-L4. n 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.

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7 ME240/105S: Product Dissection Changing Force versus Speed n Using the relationships you derived, complete the table from Session 1. n Does this agree with had previously? Why or why not? n Is the relationship between F1 and F4 constant?

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8 ME240/105S: Product Dissection 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).

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9 ME240/105S: Product Dissection Effective and Unused Force n In your journal (for extra credit), show that: Fe = Fr sin ( 1 + 2 - 3) Fp = Fr cos ( 1 + 2 - 3) Fr Fe is effective force which produces motive torque. Fu Fr-Fe = unused force.

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10 ME240/105S: Product Dissection 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.

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11 ME240/105S: Product Dissection How Pedal Forces Vary over Time

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12 ME240/105S: Product Dissection 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

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13 ME240/105S: Product Dissection Are Toe-Clips Worth the Trouble?

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14 ME240/105S: Product Dissection Pedaling Speed Optimum speed for most people is 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

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15 ME240/105S: Product Dissection Human Power Output n Most adults can deliver 0.1 HP (75 watts) continuously while pedaling which results in a typical speed of 12 mph. n Well-trained cyclists can produce 0.25 to 0.40 HP continuously resulting in 20 to 24 mph. n 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?

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16 ME240/105S: Product Dissection (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

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17 ME240/105S: Product Dissection The Forces Working Against Us Drag Force due to air resistance: F drag =C drag V 2 A C drag = 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 ~ velocity 3 )

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18 ME240/105S: Product Dissection 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

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19 ME240/105S: Product Dissection Other Forces Working Against Us n Rolling Resistance F rr =C rr x Weight Typical values for C rr : knobby tires road racing tires n Mechanical Friction (bearings, gear train) absorbs typically only 3-5% of power input if well maintained

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20 ME240/105S: Product Dissection Other Energy Absorbers n Hills (energy storage or potential energy) Change in Potential Energy = Weight x Change in elevation ( h) hh Here, the rider has stored up energy equal to the combined weight of rider and bike times the vertical distance climbed.

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21 ME240/105S: Product Dissection The First Law of Thermodynamics n Conservation of Energy, for any system: Energy in = Energy out + Change in Stored Energy SYSTEM Energy input Energy Output Internal Energy of System

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