Presentation on theme: "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."— Presentation transcript:
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?
2 ME240/105S: Product Dissection Cycling Bio-Mechanics n Basic Terminology (fill in the details as a class) –Work: –Energy: –Power: –Force: –Torque:
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
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?
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.
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.
11 ME240/105S: Product Dissection How Pedal Forces Vary over Time
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?
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 )
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
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.
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