Standard Measure

There is one metric system, based on seven units and, yes, it is consistent.

  by Stan Jakuba

This manuscript is posted on this site with the permission of the author and the editors of the ASME Mechanical Engineering magazine where most of the text was published in the 2001 April issue. For a reprint, contact falcionij@asme.org.

U.S. engineers rarely need one of the requirements for their counterparts in most countries. They typically don’t have to learn a second language. In most of the world, however, engineers are at least bilingual. Most of them speak English.

The arrangement may make it convenient for Americans to venture abroad, but it also contributes to cultural isolation. And the isolation extends to the system of measurement.

There has been an undue number of letters to the editor published in this magazine over the years criticizing the metric system for its inconsistency (as compared to the English system, presumably).

We little realize how inconsistent, illogical, and unsystematic our “system” is because we are not readily confronted with alternatives.

The inconsistencies the critics of the metric system focus on are miniscule and most are due to the system’s evolution. The evolution is inevitable. Any system that wants to keep up with the evolving society must change.

Among metric users, as in any population, there are people who do not want to accept change, or are not aware of revisions or the need for them, who prefer to cling to established ways. Inconsistencies arise, then, in the way that people use the system, not in the system itself.


METRIC SYSTEM IS A STANDARD

There indeed is one, and only one, metric system – always the latest revision of the international standard that describes it. For engineers worldwide, the standard is ISO 1000. This standard is subject to change, as any standard must be, and a user is expected to follow the latest version, which is the practice with all standards.

The standard dscribes a universal, international language of measurement.

Essentially, all units created in a coordinated manner in modern times are metric in every country of the world, including the United States. The evolution is guarded by an international committee in which the United States has participated since 1875.

It may be comforting to many to learn that the standard, in the section most people use, is not expected to change for a long time. And the last major revision took place in 1960 – two generations ago.

Note that there is no officially recognized forum for the development of any other system of units, including the English system or any version of it.

The modern system of measurement is properly called SI, not metric. SI, for the French Système International, is based on seven units, called base units, and a set of names, called prefixes, that stand for certain multiples. I

Base units measure such basic physical quantities as length, mass or time. Alone or in combination, they let mankind measure everything.


THE SEVEN BASE UNITS

m

metre, meter

length

kg

kilogram

mass

s

second

time

K

kelvin

temperature

A

ampere

electric current

mol

mole

amount of substance

cd

candela

luminous intensity


DERIVED UNITS

There are, of course, hundreds of units needed for measuring “everything,” but they are all derived from those seven. The derivation is done in a way that provides the marvelous and unique feature of SI: There are no conversion factors.

Some of the derivations were given a special name. This was applied in cases where the combination would be too long and cumbersome for frequent use, or where confusion could result. Most have been used in the English system also because no official non-metric equivalent ever existed.


DERIVED UNITS WITH SPECIAL NAMES

Bq

becquerel

radioactivity

C

coulomb

electric charge

F

farad

capacitance

Gy

gray

absorbed dose

H

henry

inductance

Hz

hertz

cycle frequency

J

joule

energy

kat

katal

molar flow

lm

lumen

luminous flux

lx

lux

luminance

N

newton

force

Ω

ohm

resistance

Pa

pascal

pressure

rad

radian

plane angle

S

siemens

conductance

sr

steradian

solid angle

Sv

sievert

dose equivalent

T

tesla

magnetic flux density

V

volt

electrical.potential (voltage)

W

watt

power

Wb

weber

magnetic flux

All derived units can be expressed in terms of the base units. The derivations are as straightforward as the relationship of length to breadth to compute area, m2. The unit newton, for example, is derived from mass times acceleration, the kilogram accelerating a meter per second per second or, in graphic symbols, kg.m/s2.

As convenient, units may be expressed in a combination of both base and derived units. Knowing that torque, for example, means force times distance leads to the newton meter, N.m. Or, for energy density (energy per mass or volume), the same logic leads to the units J/kg or J/m3. Pressure is force per area, hence the unit pascal is N/m2.

Many derived units can be expressed in more than one form, but professional use usually settles on a single convention. For example, the unit of dynamic viscosity could be expressed as kg/(m.s) or N.m2 or Pa.s. Only the last form is prevalent.


HOLDOVERS FROM THE PAST

As pointed out in the letters to the editors, there are inconsistencies in the sense that non-SI units and terms remain in local (and, in some cases, general and approved) use. They mostly reflect a tradition that is slow to die.

Here are several examples of terms carried over from the past that are still in common and approved use.

The degree Celsius (symbol °C) designates a temperature on the Celsius scale. Note that as an increment, the degree Celsius is identical to the kelvin.

The degree in plane angle (symbol °) is an alternative to the SI radian.

The liter and milliliter are the everyday usage alternates for dm3 and cm3, respectively.


HANDLING LONG NUMBERS

Prefixes (for example, kilo, centi, and milli) often precede the name of an SI unit. Prefixes were devised to shorten long numbers; for example, 20 000 kg shortens to 20 Mg, and 0.0008 A to 0.8 mA. 

Prefixes are the names of “power” multiples (hundred, thousandth, million, etc.). Their use provides an alternative to the scientific notation (50 000 expressed as 5x104), eliminates the need for the creation of unnecessary new units (5,280 feet grouped into one mile), and helps retain only significant digits.

The 10n notation is impractical for the non-scientific person, and the creation of the new units is impractical for everybody, because in the modern world it would necessitate coining thousands of names and subjecting each of us to memorizing hundreds of them.

Instead, the prefixes shorten numbers to make them convenient for everybody to use.

While the SI committee has so far established 20 prefixes, far fewer – perhaps eight – are needed in daily life and in common technical work.

Ten are more than most people need.


SELECTED PREFIXES AND THEIR MEANINGS

 

G

billion (U.S.)

giga

 

M

million

mega

 

k

thousand

kilo

*

h

hundred

hekto, hecto

*

da

ten

deka, deca

*

d

tenth

deci

*

c

hundredth

centi

 

m

thousandth

milli

 

µ

millionth

micro

 

n

billionth (U.S.)

nano

With rare exceptions, Americans consider km and mm or cm separate units. This is mainly because our schools teach converting among them. That misguided practice leads to the persistent argument against metric for having too many and long-named units.

But km or mm is just a way of saying in shorthand “a thousand meters” or “a thousandth of a meter.” One cannot convert among them as one does not convert between “a thousand inches” and “a thousandth of an inch.” Prefixes are a language – the words can be translated, not converted.

There is hope. We seem to be able to treat “kilobyte,” “megabyte,” and “gigabyte” quite comfortably without converting among them. This author has not heard as yet anyone claiming them to be three different units.

* The use of these four prefixes is declining all over the world, with hekto (hecto) and deka (deca) not in engineering use anymore, and deci and centi surviving in engineering only with m2 and m3 (and, to be picky, deci alone with the non-SI unit bel as in dB).  


GETTING TO LIKE SI

Most people, once they understand it, like SI for its logic, for featuring only one unit per physical quantity, and for its lack of conversion factors. On the other hand, some older engineers don’t like to use it. This is understandable. One dislikes anything that one does not understand and has little feel for.

The author hopes that this article has provided an understanding of the system. To get the feel of the units takes longer, and personal initiative is required.

The next table presents a sample of reference numbers in SI that an engineer may need on job and should take the time to write down. With the numbers, each unit is shown accompanied by the most suitable prefix.


PHYSICAL QUANTITIES, THEIR UNITS AND TYPICAL VALUES

Quantity Old Units SI Unit Reference Numbers

Force

ton, lb, oz.

N

M6 steel screw: 10 kN. A 102 kg man’s gravity force: 1 kN on Earth

Pressure

psi,  lb/ft2

Pa

Car tire: 200 kPa. Screw steel, tensile: 800 MPa, yield: 640 MPa

Modulus

lb/ft2, lb/in2

Pa

Young’s for steel: 200 GPa, for aluminum: 70 GPa

Heat content

Btu/lb, cal/oz.

J/kg

Hydrogen LHV: 120 MJ/kg

Torque

in-lb, ft-lb

N.m

M6 steel screw tightens to: 10 N.m

Specific heat

Btu/(lb-F)

J/(kg.K)

Aluminum: 0.90 kJ/(kg.K)

Thermal conductivity

Btu-ft/(hr-ft2-F)

W/(m.K)

Steel: 62 W/(m.K). Concrete: 1 W/(m.K). Aluminum: 50 W/(m.K)

Viscosity (kinematic)

ft2/hr

m2/s

Air: 15 mm2/s. Water: 1.1 mm2/s. Fuel oil: 3.5 mm2/s

Viscosity (dynamic)

lb/(hr-ft)

Pa.s

Air: 18 mPa.s. Water: 1.1 mPa.s. Fuel oil: 2.9 mPa.s


SEEK BREVITY AND UNIVERSALITY

SI units, prefixes, and rules were established to facilitate data communication worldwide. They represent a compromise intended to suit all languages, to ease arithmetic manipulations, to prevent ambiguity, and to retain some of the traditions of the metric system.

For technical documentation, the preferred way of writing SI prefixes and units is by their symbols; for example, 5 kg, not 5 kilograms or five kilograms.

If each symbol is written according to the SI rules – distinguishing between uppercase and lowercase letters, and between the Latin and Greek letters – it will be intelligible everywhere, regardless of the script and language a nation uses.

For reference:

For those who want to check themselves, the relationship of the specially named derived units to the base units is shown next.

Unit Base Units   Unit Base Units

 

Bq

s-1

 

Ω

m2.kg/A2.s3)

C

A.s

Pa

kg/(m.s2)

F

A2.s4/(kg.m2)

rad

m/m

Gy

m2/s2

S

A2.s3/(m2.kg)

H

m2.kg/(A2.s2)

sr

m2/m2

Hz

s-1

Sv

m2/s2

J

m2.kg/s2

T

kg/(A.s2)

kat

mol/s

V

m2.kg/(A.s3)

lm

cd.sr

W

m2.kg/s3

lx

cd.sr/m2

Wb

m2.kg/(A.s2)

N

m.kg/s2

 

 


APPENDIX: The Definitions of the Seven Units

 The Web site of the National Institute of Standards and Technology presents the following definitions of the base units. (The text is abbreviated here.)

 meter

The length of the path traveled by light in vacuum in 1/299 792 458 of a second.

kilogram

The mass of the international prototype of the kilogram.

second

The duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom. 

ampere

That constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 2x10-7 newton per meter of length.

kelvin

The fraction 1/273.16 of the temperature of the triple point of water.

mole

The amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kg of carbon 12.

candela

The luminous intensity of a source that emits monochromatic radiation of frequency 540x1012 Hz and that has a radiant intensity of 11/683 watt per steradian.

 

Stan Jakuba is president of S I Jakub Associates in West Hartford, Connecticut, USA, a firm specializing in training and consulting in international engineering standards and practices. Please direct inquiries to jakuba@alum.mit.edu.

© 2001, S I Jakub Associates and ASME

Article reformatted for HTML display. Last updated on 2001-07-16.

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