Download 2014-3 Human Power Notes

BPK201
Biomechanics
Physiological Energy, Work, Power and Efficiency
Case #1: human powered flight
A 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.
2
Case #2: human power plants
An 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.
3
Review
Linear Kinetics (Unit 5) and Angular Kinetics (Unit 6): Energy, Work,
Power, Joule, Watt, Kinetic Energy, GPE, EPE, Conservation of Energy
4
Energy
Energy 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. 5
Conservation of Energy
Energy 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.
Energy Dissipation
The 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.
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Work
Energy 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 (SodiumPotassium pumps), membrane and intracellular transport, synthetic
reactions, etc.
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Physiology & Thermodynamics
8
Units of Energy and Work
The 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 Energy
Remember: 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.
ET = EK + EP
ET = ETKE + E RKE + EGPE + EEPE
ET =
1 2 1 2
1
mv + I! + mg!h + k!x 2
2
2
2
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Example: Mechanical Energy in Walking
During 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 Work
Mechanical 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.
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!
(
)
Angular version
Wmech
! !
= T !!
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Mechanical Work: Intuition
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Example: Cardiac Mechanical Work
Estimate 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 Power
Mechanical 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.
dWmech "Wmech
Pmech =
!
dt
"t
! !
Pmech = 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! )
Angular version
Pmech
! !
= T !!
15
Mechanical Work and Mechanical Power
Ankle Joint Power during Walking
400
Power
(Watts)
positive work
200
0
0
20
40
60
80
100
negative work
% stride cycle
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Efficiency
A 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.
work output
Eff =
energy input
Eff =
power output
power input
Effchem!mech
Pmech
=
Pchem
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Isolated Muscle Efficiency
Muscles convert stored
chemical energy (fat, etc.)
into mechanical work.
Chemical Input Energy is
HEAT + MECH WORK
Efficiency is:
Effchem!mech
Wmech
=
Echem
Maximum Eff ~ 25%: 4J of
food yields 1 J of work.
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Muscle Efficiency
Mechanical work
External work
O2 uptake
Heat
Joint friction
Metabolic
work
Positive work
CO2 expired
Isometric work
Negative work
(e.g. against gravity)
(e.g. co-contraction)
Internal work
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Isolated Muscle Work Loops
20
Isolated Muscle Power
Maximum muscle power has
been characterized in
isolated muscle experiments
using a work-loop approach.
Maximum power for nonoxidative 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?
(Josephson, 1993)
21
Muscle Power - Whole Body
Power output (Watts)
>300 Watts sustained
Power output (horsepower)
nearly 2HP max
Duration (minutes)
(Wilkie, 1960)
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Efficiency - Whole Body
(Abbott, Bigland and Ritchie, 1952)
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Efficiency – Slope Walking
1J of positive muscle work will require a minimum of 4J of metabolic energy
-120% efficient
(minimum)
-1J of negative muscle
work will require a
minimum of 0.83J of
metabolic energy
+25% efficient
(maximum)
(Margaria, 1963)
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Case #1: human powered flight
A 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.
25
Case #1: human powered flight
26
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 plants
An 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.
29
Case #2: human power plants
30
4 billion people x
50 Watts x 8 hrs/day
=
11 Nuclear
Power Plants
=
< 0.5% of world’s energy needs
2008
2002
2008
2009
2010
2010
2011
2014
2014
Performance: 2014
Autonomous
Lightweight
12 Watts electrical on average
30 Watts electrical downhill
6% cost increase overall
1% cost increase for power generation