1 ME240/105S: Product Dissection Biomechanics of Cycling 1.Why do we shift gears on a bicycle? 2....
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Transcript of 1 ME240/105S: Product Dissection Biomechanics of Cycling 1.Why do we shift gears on a bicycle? 2....
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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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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
F = ma = m dv/dt
F1
F2
F3
F4
m
aC.G. A Rigid Body
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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
used by permission of Human Kinetics Books, ©1986, all rights reserved
Forces Acting on a Moving Bicycle
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ME240/105S: Product Dissection
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.
used by permission of Human Kinetics Books, ©1986, all rights reserved
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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ME240/105S: Product Dissection
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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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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ME240/105S: Product Dissection
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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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
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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ME240/105S: Product Dissection
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
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
(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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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
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.
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 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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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 upenergy equal to the combined weight of rider and bike times the vertical distance climbed.