BPK201 Biomechanics

Physiological Energy, Work, Power and Efficiency

Case #1: human powered flightA team of aeronautical engineers are building a human-powered aeroplane to fly across the Georgia Straight, from Vancouver to Victoria. You have been tasked with determining whether humans are capable of such a feat. That is, can humans generate enough power to lift their own body weight into the air and keep it there?

An incorrect answer will result in a large waste of time and money, as well as risking the pilot’s death.

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Case #2: human power plantsAn NGO has raised funds to build human power plants for generating electricity. They are trying determine whether they should use them for powering Canadian homes, thereby reducing the world’s carbon footprint, or for powering remote african villages. They have hired you to make the correct decision.

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ReviewLinear Kinetics (Unit 5) and Angular Kinetics (Unit 6): Energy, Work, Power, Joule, Watt, Kinetic Energy, GPE, EPE, Conservation of Energy

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EnergyEnergy is a property of all physical things. If it is a physical thing, it has energy. Think about it like mass. (Actually, it is more than just “like” mass: E=mc2).

There are many forms,and subforms, of energy: • chemical • mechanical (kinetic: translational, rotational, grav. potent…) • thermal • electrical • etc.

Energy can be transferred from one form to another. For example, muscle contractions are the transfer of chemical energy to mechanical energy.

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Conservation of EnergyEnergy can be transferred from one form to another. But, it cannot be created or destroyed.

This principle is called the Conservation of Energy and governs everything in our universe, including our physiology.

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Energy DissipationThe total energy in an isolated system is constant (this is just another way of saying energy is conserved), but in converting from one useful form to another, energy is also constantly converted to thermal energy (i.e. heat) due to factors like friction.

Systems can’t convert all of this thermal energy back to a useful form, thus all systems must continue to take in energy to survive.

WorkEnergy can be thought of as the capacity to do work. And work can be thought of the change in energy.

To increase the total energy of a system, work needs to be done on it. This might be to lift it, or heat it, or charge it, or form chemical compounds, or whatever.

The definition of a system is arbitrary. For example, we can think of all the blood in the body as a system. The heart needs to do mechanical work on it to increase its kinetic energy as it leaves the heart or else the blood kinetic energy will keep dissipating to heat and come to a stop.

Other examples: signal generation and conduction (Sodium-Potassium pumps), membrane and intracellular transport, synthetic reactions, etc.

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Physiology & Thermodynamics

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Units of Energy and WorkThe standard unit of energy and work is the Joule (J), defined as 1 Newton of force applied over 1 metre.

To be extra confusing, the various forms of energy we deal with on a daily basis are expressed in many different units:

• Food (1 kcal ~= 4.2 kJ) • Gasoline (litres) • Batteries (mA•hrs) • House Electricity (kW•hrs) • House Natural Gas (GJ)

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Mechanical EnergyRemember: mechanical energy is just one form of energy.

A mechanical system has kinetic energy if it is moving. Since motion can be translational or rotational, kinetic energy can be translational or rotational.

A mechanical system has potential energy if there is an external force acting on it, and the force depends on the systems position. We most commonly deal with gravitational and elastic potential energy.

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ET = EK + EP

ET = ETKE + ERKE + EGPE + EEPE

ET =12mv2 + 1

2I! 2 +mg!h + 1

2k!x2

Example: Mechanical Energy in WalkingDuring the single support phase of walking, the stance leg behaves a lot like a rigid inverted pendulum. At the beginning of single support, a 100 kg person has a center of mass speed of 1 m/s and contacts the ground with a leg angle of 30 degrees. How fast is she moving at the top of the pendular arc? How fast is she moving at toe-off when the leg returns to 30 degrees?

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Mechanical WorkMechanical work is defined as the change in mechanical energy.

It is calculated as the product of force and the displacement of the point of force application.

Mechanical work is a scalar quantity: it does not have direction.

Mechanical work can be positive or negative.

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Wmech = !ET

Wmech =!F! "ds

If force is constant, and the displacement is perpendicular to the force, then:

Wmech =!F !!d

If force is constant, and the displacement is not perpendicular, then:

Wmech =!F !!d !cos!( )

Wmech =!T !!!

Angular version

Mechanical Work: Intuition

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Example: Cardiac Mechanical WorkEstimate how much mechanical work does the heart perform with each heart beat? Things we need to know:

• Diastolic Pressure: 120 mmHg (~16,000 Pa) • End Diastolic Volume: 120 ml • Systolic Pressure: 80 mmHg (~10,500 Pa, avg: 13,250 Pa) • End Systolic Volume: 50 ml

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Mechanical PowerMechanical power is defined as the rate of change of mechanical work.

It is calculated as the product of force and the velocity of the point of force application.

Mechanical power is a scalar quantity: it does not have direction.

Mechanical power can be positive or negative.

The units of power are Watts: Joules per second.

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Pmech =dWmech

dt! "Wmech

"tPmech =

!F ! !v

If force is constant, and the velocity is perpendicular to the force, then:

Pmech =!F ! !v

If force is constant, and the displacement is not perpendicular, then:

Pmech =!F ! !v !cos!( )

Pmech =!T ! !!

Angular version

Mechanical Work and Mechanical Power

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% stride cycle

0 20 40 60 80 100

Power (Watts)

400

200

0

negative work

positive work

Ankle Joint Power during Walking

EfficiencyA dimensionless number that describes how much work you get out of a system for the energy you put in.

Another way to state the 2nd law of thermodynamics is that efficiency is always less than 100% because some of the input energy ends up as heat rather than mechanical work.

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Eff = work outputenergy input

Eff = power outputpower input

Effchem!mech =PmechPchem

Isolated Muscle EfficiencyMuscles convert stored chemical energy (fat, etc.) into mechanical work.

Chemical Input Energy is HEAT + MECH WORK

Efficiency is:

Maximum Eff ~ 25%: 4J of food yields 1 J of work.

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Effchem!mech =Wmech

Echem

Muscle Efficiency

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Metabolic work

O2 uptake

CO2 expired

Positive work

Mechanical work

Heat

Isometric work (e.g. against gravity)

Negative work (e.g. co-contraction)

Joint friction

External work

Internal work

Isolated Muscle Work Loops

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(Josephson, 1993)

Isolated Muscle PowerMaximum muscle power has been characterized in isolated muscle experiments using a work-loop approach.

Maximum power for non-oxidative efforts is ~150 W/kg

Maximum sustained power is ~ 100 W/kg.

Average person ~65 kg and ~40% muscle: 2.6kW sustained! Is this possible?

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Muscle Power - Whole Body

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Pow

er o

utpu

t (W

atts

)Pow

er output (horsepower)

Duration (minutes)

(Wilkie, 1960)

nearly 2HP max

>300 Watts sustained

(Abbott, Bigland and Ritchie, 1952)23

Efficiency - Whole Body

Efficiency – Slope Walking

(Margaria, 1963)

1J of positive muscle work will require a minimum of 4J of metabolic energy

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-1J of negative muscle work will require a

minimum of 0.83J of metabolic energy

-120% efficient (minimum)

+25% efficient (maximum)

Case #1: human powered flightA team of aeronautical engineers are building a human-powered aeroplane to fly across the Georgia Straight, from Vancouver to Victoria. You have been tasked with determining whether humans are capable of such a feat. That is, can humans generate enough power to lift their own body weight into the air and keep it there?

An incorrect answer will result in a large waste of time and money, as well as risking the pilot’s death.

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Case #1: human powered flight

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Gossamer Albatross • Crew: 1 • Length: 10.36 m (34.0 ft.) • Wingspan: 29.77 m (97.7 ft.) • Height: 4.88 m (16.0 ft.) • Wing area: 45.34 m2 (488 ft2) • Empty weight: 32 kg (70 lb) • Loaded weight: 97.5 kg (215 lb) • Useful load: 65.5 kg (145 lb) Performance • Maximum speed: 28.97 km/h (18 mph) • Distance from Vancouver to Victoria 120 km (about 4 hours)

Case #2: human power plantsAn NGO has raised funds to build human power plants for generating electricity. They are trying determine whether they should use them for powering Canadian homes, thereby reducing the world’s carbon footprint, or for powering remote african villages. They have hired you to make the correct decision.

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Case #2: human power plants

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4 billion people x 50 Watts x 8 hrs/day

= 11 NuclearPower Plants

< 0.5% of world’s energy

needs=

2008

2002 2008 2009 2010

2010 2011 2014 2014

Autonomous

Lightweight

12 Watts electrical on average

30 Watts electrical downhill

6% cost increase overall

1% cost increase for power generation

Performance: 2014