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

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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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Cycling Bio-Mechanics

Basic Terminology (fill in the details as a class)

– Work:

– Energy:

– Power:

– Force:

– Torque:

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Newton’s Second Law

F = ma = m dv/dt

F1

F2

F3

F4

m

aC.G. A Rigid Body

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Forces Acting on a Bicycle at Rest

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

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Forces Acting on a Moving Bicycle

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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.


Purpose of bike transmissionis 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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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?

Increase in: Effect on Output Force Effect on Output Speedfront chain ring (# of teeth)

rear cog (# of teeth)

rear wheel (diameter)

crank arm length

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Ankling


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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Effective and Unused Force

In your journal (for extra credit), show that:

Fe = Fr sin (1 + 2 -3)

Fp = Fr cos (1 + 2 -3)

FrFe is effective force which produces motive torque.

Fu Fr-Fe = unused force.

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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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How Pedal Forces Vary over Time

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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)


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Are Toe-Clips Worth the Trouble?

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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 EFFICIENTPEDALLING SPEED


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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?

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(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.


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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 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)

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SomeEmpirical

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.


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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

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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 upenergy equal to the combined weight of rider and bike times the vertical distance climbed.

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The First Law of Thermodynamics

Conservation of Energy, for any system:

Energyin = Energyout + Change in Stored Energy

SYSTEM

Energy input

Energy Output

Internal Energyof System

Documents

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