The Measure of
All Things
ABE425 Engineering Measurement
Systems
Dr. Tony Grift
History of
Le Système International d’unités
1791 March 30 —the new definition for the meter be equal to one tenmillionth of the length of the Earth's meridian along a quadrant through
Paris, that is the distance from the equator to the north pole.
Delambre
Méchain
Triangulation using the Borda repeating circle improved
precision markedly by repeated observations
Repeating circle surveying
instrument
During the “Terror” (1793-1794), the guillotine was
used to execute more than 3,000 people per month
Execution of Maximilien
Robespierre, leader of the
French Revolution, 1794
Dr. Joseph Guillotin
The SI system was formalized in the Convention du
Mètre, a treaty among 51 nations (2008)
The International Bureau of Weights and Measures is an
international standards organization, one of three such organizations
established to maintain the International System of Units (SI)
under the terms of the “Treaty of the meter” (Convention du Mètre).
The organization is usually referred to by its French initials, BIPM
(Bureau International des Poids et Mesures).
The BIPM was created on 20 May 1875, following the signing of the
meter Convention, a treaty among 51 nations (as of August 2008). It is
based at the Pavillon de Breteuil in Sèvres, France, where it enjoys
extraterritorial status.
The seven base unit definitions
1.
2.
3.
4.
5.
6.
7.
Length (distance)
Mass
Time (duration)
Electric current
Temperature
Matter
Luminous intensity (candela)
Base units are defined, based on elementary physics
relationships, but how can they be realized in a primary
standard?
How many direct electric units are there? Does this surprise
you?
Length definition: Meter
1790 — The French National Assembly decides that the length of the new
meter would be equal to the length of a pendulum with a half-period of
one second.
1791 — The new definition for the meter be equal to one ten-millionth of
the length of the Earth's meridian along a quadrant through Paris, that is
the distance from the equator to the north pole.
1795 — Provisional meter bar constructed of brass.
1799 — The French National Assembly specifies the platinum meter bar,
as the final standard.
1889 — The International Committee for Weights and Measures
Committee Generale des Poids et Mesures (CGPM) defines the meter as the
distance between two lines on a standard bar of an alloy of platinum with
ten percent iridium, measured at the melting point of ice.
1927 — The seventh CGPM adjusts the definition
of the meter to be the distance, at 0 °C, between
the axes of the two central lines marked on the
prototype bar of platinum-iridium, this bar being
subject to one standard atmosphere of
pressure and supported on two cylinders of at
least one centimeter diameter, symmetrically
placed in the same horizontal plane at a distance
prototype bar of platinum-iridium
of 571 millimeters from each other.
Length definition: Meter cont.
1960 — The eleventh International Committee for Weights and
Measures defines the meter to be equal to 1,650,763.73 wavelengths
in vacuum of the radiation corresponding to the transition between the
2p10 and 5d5 quantum levels (resonance) of the krypton-86 atom.
1983 — The seventeenth CGPM defines the meter as equal to the
distance travelled by light in vacuum during a time interval of
1⁄299,792,458 of a second.
2002 — The International Committee for Weights and Measures
(CIPM) recommends this definition be restricted to “lengths ℓ which are
sufficiently short for the effects predicted by general relativity to be
negligible with respect to the uncertainties of realization.”
Mass definition: kilogram
The kilogram was originally defined as the mass of one litre (or,
equivalently, 1 dm3) of water (ice) at its melting point. This definition
was later revised to specify a temperature of 4 °C.
Mass is the only standard still based on a physical object. There are
several proposed methods to link the kg to universal constants.
Mass is the only standard that has a prefix (kilo) for historical reasons:
Originally the kilogram was called the "grave", and the "gram" was an
alternative name for a thousandth of a grave. After the French Revolution,
the word "grave" carried negative connotations from the “Ancien Regime”,
as a synonym for the title "count". The grave was renamed the kilogram.
Mass definition : Platinum-iridium international prototype
of the kilogram (IPK) kept in Sèvres (near Paris), France
Since 1889, the SI system defines the
magnitude of the kilogram to be equal to
the mass of the International Prototype
Kilogram or “IPK”.
The IPK is made of a platinum alloy known
as “Pt-10Ir”, which is 90% platinum and
10% iridium (by mass) and is machined into
a right-circular cylinder (height =
diameter) of 39.17 millimeters to minimize
its surface area.
Mass definition: Platinum-iridium international prototype
of the kilogram (IPK) kept in Sèvres (near Paris), France
The IPK and its six sister copies are stored
at the International Bureau of Weights and
Measures (BIPM) in an environmentally
monitored safe in the lower vault located in
the basement of the BIPM’s House of
Breteuil in Sèvres on the outskirts of Paris.
Three independently controlled keys are
required to open the vault. 40 official copies
of the IPK were made available to other
nations (the USA got three) to serve as
their national standards. These are
compared to the IPK roughly every 50
years.
The second had been based on a pendulum clock since
1658 to split a day in 24 hrs / 60 min / 60 sec
In 1793, the Revolutionary Government in
France decreed that the day should be
Divided into 10 hours of 100 minutes, and
the year into 10 months of 30 days.
A pendulum clock built by Dutchman
Christiaan Huygens, inventor of the
pendulum clock (Horologium Oscillatorium),
around 1658.
Definition of Electric current (Ampere)
Ampere (A): The ampere is that constant current which, if
maintained in two straight parallel conductors of infinite
length, of negligible circular cross section, and placed 1
meter apart in vacuum, would produce between these
conductors a force equal to 2*10-7 Newton per meter of length.
The definition provides a link between electric current and
force (Newton) which is related to kilogram, meter and second.
This definition may be theoretically correct, but it is
impossible to build an accurate realization.
Ampere balance
The ampere balance (also current balance or Kelvin balance) is
an electromechanical apparatus used for the precise
measurement of the SI unit of electric current, the ampere. The
magnetic force between the two coils is measured by
the amount of weight needed on the other arm of the
balance to keep it in equilibrium. The accuracy of the
current measurement is limited by the accuracy with which the
coils can be measured, and their mechanical rigidity.
Temperature in Kelvin
kelvin (K): The kelvin, unit of thermodynamic temperature, is
the fraction 1/273.16 of the thermodynamic temperature of
the triple point of water.
The International Temperature Scale of 1990 (ITS-90) is
defined by two points: the absolute zero point (0 K or -273.15
°C) and the thermodynamic temperature of the water triple
point, which is 273.16 K or 0.01 °C.
There are many other reference points along the ITS-90 scale
such as triple points, melting points and freezing points of
metals
Matter (in mole)
In chemistry and physics, the Avogadro constant (symbols: L,
NA) is the number of "elementary entities" (usually atoms or
molecules) in one mole, that is (from the definition of the mole),
the number of atoms in exactly 12 grams of carbon-12.
The link with C-12 is artificial, and it links the Mole to the kg,
which is a bad idea, since it is an artifact.
NIST: “Traceability requires the establishment of an unbroken chain
of comparisons to stated references each with a stated uncertainty “
The Système International is a beautiful
consistent theoretical framework, but it is not in
all cases conducive to realization.
The culprits are the kg and the Ampere, but also
the Kelvin and the Mole, neither of which is
linked to a universal constant.
Realization of the Length Unit meter
The realization of the meter is conducted by means of lasers of
a known and highly stable frequency. The primary standard
consists of a helium-neon laser. The optical frequency of the
laser is monitored by atomic clocks (realization of the second).
The relative uncertainty of the meter realization with iodinestabilized HeNe lasers is 2.5*10-11, which corresponds to 1 mm
in the circumference of the Earth.
‘Realization’ of the kg
40 copies of the original kg
were made and they all
vary in mass now. They
gain mass through
adsorption of atmospheric
contamination onto their
surfaces and lose mass due
to cleaning.
K48, came from the second
batch of kilogram replicas to
be produced. It was delivered
to Denmark in 1949 with an
official mass of 1 kg+81 µg.
Still, its mass and that of the
IPK diverged markedly in only
40 years; the mass of K48 was
certified as 1 kg+112 µg
during the 1988–1992 periodic
verification.
Realization of the second, using atomic clocks
Time: The second is the duration of 9 192 631 770 periods of the
radiation corresponding to the transition between two hyperfine levels
of the ground state of the cesium 133 atom.
In this instrument the frequency of a signal produced by a quartz
oscillator is compared and adjusted to the resonance-frequency of a
given transition in selected atoms. State of the art primary frequency
standards exhibit a relative frequency uncertainty of 1e-15.
Realization of the second, using atomic clocks cont.
Atomic clock on a chip (NIST)
NIST-F1 is a cesium fountain
atomic clock that serves as the
United States' primary time
and frequency standard. It is
so accurate that it will neither
gain nor lose one second in
more than 60 million
years.
Realization of an Electro Motive Force Volt standard
(Weston Cell)
The Weston cell, invented by Edward Weston in 1893, is a wetchemical cell (battery) that produces a highly stable voltage
suitable as a laboratory standard for calibration of voltmeters. It
was adopted as the International Standard in 1911.
The Josephson junction is now used as the standard for
the Electro Motive Force (Volt)
In precision metrology, the Josephson effect provides an
exactly reproducible conversion between frequency
and voltage. Since the frequency is already defined
precisely by the cesium standard, the Josephson effect is
used, to give the definition of a volt (although, as of
July 2007, this is not the official BIPM definition)
Dr. Brian Josephson
(Nobel prize, 1973, now ‘pioneer of the paranormal’)
Vn  n * f *
h
2e
n  integer
f  frequency
h  Planck's constant
e  Elementary charge of an electron
f * h  Energy in the microwave radiation
Josephson constant
Kj 
2e
h
One-volt NIST Josephson Junction array standard having
3020 junctions.
This device operates at liquidhelium temperatures (4.2K).
Microwave energy is fed through
the fin-guide structure at the
left.
Josephson standard in a
national calibration lab
(METAS in Switzerland) The
standard at METAS permits
calibrations in the voltage
range of -10 V to +10 V. At a
level of 1.018 V, the
measurement uncertainty
of the system is ±5 nV.
The Quantum Hall Effect is now used as the standard for
resistance in Ohm
Dr. Klaus Von Klitzing
(Nobel prize, 1985)
A voltage V drives a current I in the positive x direction. Normal
Ohmic resistance is V / I. A magnetic field in the positive z
direction shifts positive charge carriers in the negative y
direction. This generates a Hall potential ( VH) and a Hall
resistance (VH/ I ) in the y direction. (Kosmos, 1986)
The Quantum Hall Effect produces quantized steps in
resistance as a function of the magnetic field strength
The resistance of this material in Ohm is quantized as a function of
the magnetic field (Tesla) applied. The steps occur at resistance
values that do not depend on the properties of the material
but are given by a combination of fundamental physical
constants multiplied by an integer.
e2
where e is the elementary charge of an electron   n
h
(1.602 176 487(40)×10−19 Coulomb and h is
Planck's constant. n is integer.
The resistance unit Rk, roughly
equal to 25,812.8 ohms, is
referred to as the Von Klitzing
constant
h
Rk  2 =25812.807  
e
The Coulomb is now related to the Volt and Ohm
standards and so is the Farad and Ampere
The Josephson junction Volt standard, and Quantum Hall resistance standard (Von
Klitzing constant) allow redefinition of the charge unit Coulomb which is
equal to the charge of 6.241 509 629 152 65 * 1018 electrons
2e
 Hz  
=4.835979*1014 

h
 Volt   K * R  2e * h  2  e  2
 j k
2
h
e
e
Kj * Rk
h
4

Rk  2 =2.5812807*10   

e
Kj 
C
1
 6.241 509 629 152 65*1018
e
The capacitance unit Farad can be derived from this unit as well:
F
C
V
Most importantly, the ampere (now linked to a force in N) can be redefined as
the Coulomb per second:
A
C
s
Millikan’s experiment gave the charge of a single electron
which can be validated against Hall & Josephson effects
The experiment entailed balancing the downward
gravitational force with the upward buoyant and electric
forces on tiny charged droplets of oil suspended between two
metal electrodes.
By repeating the experiment for many droplets, he confirmed
that the charges were all multiples of a fundamental
value, and calculated it to be 1.5924(17)×10-19 C, within
one percent of the currently accepted value of 1.602
176 487 (40)×10-19 C. They proposed that this was the
charge of a single electron.
2
e
Kj * Rk
The future of the SI system
How to modernize the SI system
Define base units on realizations
Meter based on speed of light
Second based on atomic resonance frequency of cesium 133
Volt based on Josephson effect
Electrical Resistance in Ohm based on Quantum Hall effect
Amount of substance, based on Avogadro’s number
Thermodynamic temperature based on Boltzmann’s constant
Spectral luminous efficacy based on K  555 
Proposed alternatives
1. Explicit constant definition: Fix all known constants and
associate each unit with a constant
2. Explicit unit definition: Fix all known constants but do not
associate each unit with a single constant
3. ‘Bake your own pizza”. Do as you please, link any unit with any
physical constant, CGPM will provide ‘preferred methods’.
Mills, I.M., Mohr, P.J., Quinn, T.J., Taylor, B.N., Williams, E.R. 2006.
Redefinition of the kilogram, ampere, kelvin and mole: a proposed approach to
implementing CIPM recommendation 1 (CI-2005). Metrologia 43: 227-246,
doi:10.1088/0026-1394/43/3/006
Proposed alternative 1: Explicit constant definitions
1. Second: ground state hyperfine
splitting transition frequency of cesium
133 atom
2. Meter: Speed of light in vacuum (this
value has already been fixed)
3. Kg: Planck’s constant
4. Ampere: Elementary charge of an
electron
5. Temperature: Boltzmann’s constant
6. Mole: Avogrado’s constant
7. Candela: spectral luminous efficacy of
monochromatic radiation of frequency


133
Cs

hfs
 9 191 631 770 s 1
c0  299 792 458 ms -1
h = 6.626 0693(11) × 10-34 J s
e = 1.602 176 53(14) × 10-19 C
k = 1.380 6505(24) × 10-23 JK -1
N A = 6.022 1415(10) × 1023 mol-1
K  555   683 lumens Watt 1
“Such that’ construct: The International System of Units, the SI, is the system
of units scaled such that the speed of light in vacuum c0 is exactly 299 792
458 metres per second, or such that the Planck constant is exactly…..
kg derived??
kg
Mass
Speed of light
c0  299 792 458  ms 1 
meter
kg=Ns2/m
LENGTH
If all base units
would be defined
based on known
universal constants,
the kg can become
a derived unit. How
do we make a
realization though?
Electrical and
mechanical power
are equal, can we
couple them in
some kind of
electric motor
device?
Resonance Cesium atom



CS  9 191 631 770  s 1 
133
second
Coulomb C=A*s
Electric
Charge
Farad F=(C/V) Newton
Capaci
Force
tance
N=J/m
TIME
Kj 
2e
h
Josephson junction
KJ 
2e
 Hz 
 4.835979*1014  
h
V 
Volt
Ampere A=V/  ) Joule J=W*s=Nm
Electric
Energy
Current
(Work)
VOLT
RK 
h
e2
Quantum Hall Effect
h
RK  2  25,812.807
e
Ohm
Watt
Power
W=V*A=J/s
RESISTANCE
Boltzmann constant
k  1.3 806 505  JK 1 
Kelvin
THERMODYNAMIC
TEMPERATURE
Millikan charge of single
electron experiment
e  1.60217653*1019 Coulomb
K J * RK e h 1
 * 2  C
2
h e
e
Spectral luminance
K  555   683 lumensW 1 
Candela
LUMINOUS
INTENSITY
Avogadro constant
N A  6.0221415*1023  mol 1 
mol
Multiply by
AMOUNT OF
SUBSTANCE
Divide by
Redefine the kilogram
using a Watt Balance
In the NIST watt balance experiment, a
kilogram test mass is placed on a balance
pan that is connected to a coil of copper
wire, which surrounds a superconducting
electromagnet. If electric current is sent
through the coil, then just as in an electric
motor, electromagnetic forces are
produced to balance the weight of the
test mass. The apparatus measures this
current and force. The apparatus also
can move the coil vertically, and, like an
electric generator, that induces a voltage.
The velocity and voltage of the coil also
are measured. These four measurements
determine the relationship between
mechanical and electrical power,
which can be combined with other basic
properties of nature to redefine the
kilogram.
F *v  V * A
The proposition of the Avogadro Project is to redefine the
kilogram in terms of the Avogadro constant.
By current definition, an Avogadro number of
Carbon-12 atoms weigh exactly 12 grams. As
such, the kilogram could be defined as the mass
of 1000/12 * Avogadro's number of Carbon-12
atoms. The Avogadro constant itself is obtained
from the ratio of the molar mass to the mass of
an atom. For a crystalline structure such as
silicon, the atomic volume is obtained from the
lattice parameter and the number of atoms per
unit cell. The atomic mass is then the product
of the volume and density.
The nominal diameter of a 1 kg Silicon sphere is
93.6 mm. In order to obtain an accuracy of
0.01 ppm in volume, the diameter must be
known to a range of 0.6 nm, in other
words, within one atom spacing. The
roundness delta of the finished sphere is about
50 nm on a 93.6 mm diameter. It is believed
to be the roundest object in the world.
The English‘unit system’
What’s wrong with it, or what isn’t?
Many units for the same thing. Volume: gallon, liquid quart,
dry quart, liquid pint, dry pint, fluid ounce, teaspoon,
tablespoon, minim, fluid dram, gill, peck, bushel.
Strange conversions among many units. Johnny, there are 16 ounces
in a pound, 12 inches in a foot, and 3 feet in a yard. Poor Johnny.
You cannot remember all these conversion factors and why would
you, it makes no sense anyway! If you cannot remember the
conversions, how can you remember the formula? You don’t, you just
look it up. Now what if your problem isn’t in the book?
No realistic measure of small weights (lbs-oz- ??)
You need dual sets of tools to work on your car
People mix and match: we had 1/10 of an inch of rain. Our building
uses 4,100 kgal of cooling water per year
Many costly mistakes are linked to conversion issues, 125 million
dollar Mars explorer, aircraft running out of fuel in midair, leaking
seals in a nuclear power plant….
The awful invention of the ‘gauge’!!!
Metric is for nerds! This causes a schism between the nerdy crowd
and the “blue collar” crew.
The persistent English unit system makes us look dumb and
backward..
Things that make us look smart,
innovative and modern
The ENGLISH
UNIT SYSTEM
Forget Burma (Myanmar) and Liberia. The United States
is the only developed country that is not officially metric!
Lbs, oz, grain
Inch, foot, yard, mile, rod
Assignment
Mass
LENGTH
Repeat the definition
of units using the
ENGLISH unit system.
Electric
Charge
Capaci
tance
TIME
Force
Lbs, slug
Electric
Current
VOLT
Energy
(Work)
BTU
HP
Power
RESISTANCE
THERMODYNAMIC
TEMPERATURE
LUMINOUS
INTENSITY
Multiply by
AMOUNT OF
SUBSTANCE
The English unit system has NO STANDARDS !!!
Divide by
The most important thing to remember
The English unit system HAS TO GO!!! It is OUR
responsibility and duty as (future) educators to
cure this country from this illness.
Let’s make Metric Day a
departmental day of celebration
10/10/10 !!!!
This will happen only once in your
lifetime!