Presentation on theme: "Biomechanics of Cycling"— Presentation transcript:
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 isW= Fs s where Fs is the component of force in the direction of s and s is the distance movedUnits of Work: lb-ft BritishJoule (N-m) mkserg (dyne-cm) cgsother forms: calorie = J = .239 W- sec, (note the number of calories listed on your cereal box are really in units of kilocalories)Kw-hrBTU = 778 ft-lb=252 caloriesPower is the rate of doing workP=work done/time taken = F s/tAlso = F * velocity = Torque * rotational speed (radians/sec)Units: HP = 550 lb-ft/secWatt (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.
9 Effective and Unused Force Fe is effective force which produces motive torque.Fu º Fr-Fe = unused force.FrIn 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.
15 Human Power OutputMost 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?
17 The Forces Working Against Us Drag Force due to air resistance:Fdrag =CdragV2 ACdrag = drag coefficient (a function of the shape of the body and the density of the fluid)A = frontal area of bodyV = velocitySince: Power = Force x Velocityto double your speed requires 8 times as much power just to overcome air drag (since power ~ velocity3)
19 Other Forces Working Against Us Rolling Resistance Frr=Crr x WeightTypical values for Crr:knobby tiresroad racing tiresMechanical 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)hHere, the rider has stored upenergy equal to the combinedweight of rider and bike timesthe vertical distance climbed.
21 The First Law of Thermodynamics Conservation of Energy, for any system:Energyin = Energyout + Change in Stored EnergyEnergy inputInternal Energyof SystemEnergy OutputSYSTEM
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