Transcript Cycling Bio-Mechanics - Penn State Mechanical Engineering

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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ME240/105S: Product Dissection
Cycling Bio-Mechanics

Basic Terminology (fill in the details as a class)
– Work:
– Energy:
– Power:
– Force:
– Torque:
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ME240/105S: Product Dissection
Newton’s Second Law
SF = ma = m dv/dt
F4
F1
m
C.G.
a
A Rigid Body
F2
F3
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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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ME240/105S: Product Dissection
Forces Acting on a Moving Bicycle
used by permission of Human Kinetics Books,
©1986, all rights reserved
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ME240/105S: Product Dissection
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.
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ME240/105S: Product Dissection
Changing Force versus Speed

Using the relationships you derived, complete the
table from Session 1.
Increase in:
front chain ring (# of teeth)
Effect on Output Force
Effect on Output Speed
rear cog (# of teeth)
rear wheel (diameter)
crank arm length


Does this agree with had previously? Why or
why not?
Is the relationship between F1 and F4 constant?
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ME240/105S: Product Dissection
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
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ME240/105S: Product Dissection
Effective and Unused Force
Fe is effective force which
produces motive torque.
Fr
Fu  Fr-Fe = unused force.

In your journal (for extra credit), show that:
Fe = Fr sin (q1 + q2 -q3)
Fp = Fr cos (q1 + q2 -q3)
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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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ME240/105S: Product Dissection
How Pedal Forces Vary over Time
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ME240/105S: Product Dissection
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)
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ME240/105S: Product Dissection
Are Toe-Clips Worth the Trouble?
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ME240/105S: Product Dissection
Pedaling Speed
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
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ME240/105S: Product Dissection
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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ME240/105S: Product Dissection
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)
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ME240/105S: Product Dissection
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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ME240/105S: Product Dissection
Some
Empirical
Data
Drag force on a cycle versus speed
showing the effect of rider position.
(ref 3, pg 126)
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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ME240/105S: Product Dissection
Other Forces Working Against Us

Rolling Resistance Frr=Crr x Weight
Typical values for Crr:
knobby tires
road racing tires

0.014
0.004
Mechanical Friction (bearings, gear train)
absorbs typically only 3-5% of power input if well maintained
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ME240/105S: Product Dissection
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.
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ME240/105S: Product Dissection
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
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