1. 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?

2. Cycling Bio-Mechanics
Basic Terminology (fill in the details as a class)
Work:
Energy:
Power:
Force:
Torque:
Work/Energy Work is done on an object if a nonzero component of the force exists in the direction of motion. The magnitude of the work is
W= Fs s where Fs is the component of force in the direction of s and s is the distance moved
Units of Work: lb-ft British
Joule (N-m) mks
erg (dyne-cm) cgs
other forms: calorie = J = .239 W- sec, (note the number of calories listed on your cereal box are really in units of kilocalories)
Kw-hr
BTU = 778 ft-lb=252 calories
Power is the rate of doing work
P=work done/time taken = F s/t
Also = F * velocity = Torque * rotational speed (radians/sec)
Units: HP = 550 lb-ft/sec
Watt (Joule/sec)
HP = 746 Watts

3. Newton’s Second Law SF = ma = m dv/dt F4 F1 m F2 F3 a A Rigid Body
C.G.

4. Forces Acting on a Bicycle at Rest
used by permission of Human Kinetics Books,
©1986, all rights reserved

5. Forces Acting on a Moving Bicycle
used by permission of Human Kinetics Books,
©1986, all rights reserved

6. 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.

7. 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?

8. 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

9. Effective and Unused Force
Fe is effective force which produces motive torque.
Fu º Fr-Fe = unused force. Fr
In your journal (for extra credit), show that:
Fe = Fr sin (q1 + q2 -q3)
Fp = Fr cos (q1 + q2 -q3)

10. 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.

11. How Pedal Forces Vary over Time

12. 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)

13. Are Toe-Clips Worth the Trouble?

14. Pedaling Speed Optimum speed for most people is 55-85 rpm.
MOST EFFICIENT
PEDALLING SPEED
Optimum speed for most people is 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

15. 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?

16. 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)

17. 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)

18. Some Empirical Data
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.
(ref 3, pg 126)
used by permission of Human Kinetics Books,
©1986, all rights reserved

19. Other Forces Working Against Us
Rolling Resistance Frr=Crr x Weight
Typical values for Crr:
knobby tires
road racing tires
Mechanical Friction (bearings, gear train)
absorbs typically only 3-5% of power input if well maintained

20. 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.

21. 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