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SI

Why SI?

SI or not SI is one of those arguments that does not have an obvious winner; it all depends on the relative importance you place on different views. Let's look at five points:

Tradition and History

Many of our "old" units can trace their ancestry back thousands of years. The best way of preserving this history might be to continue using them. This argument loses some of its force as many of the old units are already rarely used (perches, quarters, gills) and the rest are gradually being rationalised. In my opinion, the best place to preserve old things is in a museum, but I know others disagree.

In the UK, it does not help that metric is seen as a French invention.

Daily life

There's no doubt that the traditional units are very well designed for day-to-day simple tasks. They are just the right size for measuring drinks, corn, fields, buildings, roads and so on because that is what they were made for. Even the names, typically easy-to-say short words, are more convenient. Anyone whose life does not extend beyond buying apples in the local shop will see no advantage in SI, and that's difficult to gainsay.

Engineering

It is possible to design all sorts of things in either set of units, though there is a strong tendency to rationalise the old units. Sometimes, the SI prefix idea is retro-fitted back onto the old system, to produce micro-inches or kilo-feet. This is a strong sign that the old system is inadequate in many situations where new fields take us away from the human scale. There is also the need to invent new "old" units, such as poundals, slugs and horse-power, to cover measurements that the old system was never designed for.

International trade

Working in the UK, it is now generally possible to assume the world is metric, provided one avoids US suppliers. I have on occasions had to write "warning - inches" on US drawings that we've received. If US stuff comes into our lab with non-metric threads, we have to rummage in the odds-and-ends box to find something to fit. Any company that refuses to recognise metric these days is handicapped, unless it is so big that it controls its marketplace.

Difficult calculations and understanding

Several things attract me to SI, but most important are the clarity of definition, and the internal self-consistency.

The old units were related to human features, or arbitrary, in general could not be defined except by a prototype, and could not be reproduced except by direct reference to the prototype. From the invention of metric, it was seen to be important to relate units to some external constant. The metre was defined as one ten-millionth of the distance from the North pole to the equator through Paris, something not expected to change, and therefore a standard metre could be re-created anywhere at any time. The same was not then possible for the kilogram, which was defined by a prototype, though it could be easily approximated from the metre and the density of water. This process has continued, so that the current definitions [1] are based on atomic properties that are thought to be constant throughout the universe. This is a beautiful idea. We could define our system of units to a green man on Mars, and he could construct examples, without ever seeing the originals.

The self-consistency is even more important. In the old system, new units were invented as they were needed, independently in many fields. Even with simple measurement of volume there were linear-based units such as cubic yards or acre-feet, and special units such as gallons or hogsheads. Often these were originally unrelated, and were only fixed relative to each other fairly recently. Worse happened in the mechanical units, where different units of work (foot-pound, foot-poundal, BTU) and power (horse-power, BTU/hour) arose. Not only are these units unrelated to each other, but they ignore the underlying theory. Take the foot-pound: work is a force times a distance; pound is a unit of mass; the unit assumes that a mass has a fixed weight whereas in reality it varies with location. So either we have to to define the foot-pound at a particular place and time, or measurement of horse-power will vary depending on location. This is horrible.

This lack of relation to the theory also complicates the formulae used to calculate mechanical quantities. Not only are there un-needed conversion constants, but unwanted physical factors, such as the strength of gravity in the power units, crop up too. It is almost always easier, for any non-trivial calculation, to convert everything into SI, calculate, then (if necessary!) convert the answer back.

Old units hinder general understanding. For example, it is customary (in the UK) to measure the mass of babies in pounds, of adults in stones, and of cars in tons or hundredweights; this adds an extra layer which has to removed to see how babies compare with adults, or how much of the proportion of the weight of a car comes from the occupants. Similar problems, but much more significant, occur as the comparisons get more remote from experience.

SI

So, I'm convinced by SI, and have been convinced by metric in general for the last thirty years. Many, though, are influenced by the history argument, and many more by the convenience of old units in simple daily activity. The more one uses measurements, and thinks quantitatively about the world, and talks to people in other walks of life, the more SI is attractive. It will win!

[1] Except for the kilogram, which is very nearly there.

Conversions of old units into SI

(Values in bold are exact.)

unitvalue in SI unitnotes
acre4046.856 422 4 m2a chain by a furlong - 4840 sq yds
acre-foot1233.5 m3
amu1.492e-10 Jatomic mass unit
angstrom1e-10 m
au149 597 870 700 mastronomical unit (defined Sep 2012)
atmosphere101 325 Pa
bar100 000 Pa
barley corn (length)0.008 466.. m3 to the inch (shoe sizes)
barrel (beer)0.163 66 m336 UKgall
barrel (oil)0.159 m3
board foot0.002 359 7 m312*12*1 inch (US)
Britsh thermal unit (BTU)1055.1 J
BTU (international)1055.05585262 J
BTU per minute17.584 W
BTU per hour0.293 07 W
bushel (UK capacity)0.036 369 m38 UKgall
bushel (US capacity)0.035 239 m32150.42 in3
butt (beer) 0.491 m3108 UKgall
butt (wine) 0.573 m3126 UKgall
Calorie (food)4186.8 J
calorie4.1868 J
carat (metric)2e-4 kg
centipoise0.001 Pa.sCGS viscosity
chain20.1168 m
chaldron1295 kgcoal
clove3.175 kg7 lb wool, cheese; also 8 lb or 10 lb
cord3.62 m38*4*4ft (timber, US)
cord2.2 m38*4*4ft * ~62% fill (US)
cord foot0.453 m316ft3 (US)
cran0.170 48 m3herrings
cubic foot0.028 316 846 592 m3
cubic inch1.638 706 4e-4 m3
cubic mile4.1682e9 m3
cubic yard0.836 127 36 m3
cubit0.4633 mEgyptian common cubit
cup (US)2.3659e-4 m3
day86 400 s
degree (arc)0.017 453 rad
degree Celsius1 Koffset zero: 0 degC at 273.15K
degree Centigrade1 Koffset zero: 0 degC at 273.15K
degree Fahrenheit0.555.. Koffset zero: 0 degF at 255.37K
degree Rankine0.555.. K
degree Reamur?1.25 Koffset zero: 0 degR at 273.15K
dirhem0.003 11 kgancient Egypt
dozen12
drachm0.003 887 9 kg
dram avoirdupois0.001 771 8 kg16 to the ounce
dyne1e-5 N
ell (NL)0.6858 m
ell (Scotland)0.944 88 m
ell (UK)1.143 m45 inches
electron-volt1.6021e-19 J
erg1e-7 J
esu3.336e-10 Celectrostatic unit
fathom1.8288 m6 feet
firkin (beer)0.040 915 m39 UKgall
firkin (butter)25.401 kg
fluid drachm (UK)3.5516e-6 m3
fluid ounce (UK)2.8413e-5 m3
fluid ounce (US)2.9574e-5 m3
foot0.3048 m
foot (US survey)0.304 800 6 mdefinition 1200/3937 m
foot-lambert3.4263 cdm-2 1/(pi*0.30482)
foot-lbf1.3558 Nmtorque
foot-pound1.3558 Jenergy
foot-pound per second1.3558 W
fortnight1 209 600 s
furlong201.168 m
gal0.01 ms-21 cm/s/s, vibrations (Japan?)
gallon (UK)0.004 546 09 m31995
gallon (US dry)0.004 404 88 m3268.8025 cubic inches
gallon (US liquid)0.003 785 4 m3231 cubic inches
gallon (old wine)0.003 785 m3
gauss1e-4 T
gill (UK)1.4207e-4 m34 to UK pint
grain6.479 891e-5 kg1/7000 lb
grain (drugs)6e-5 kgdefinition (in UK, Weights & Measures Act, 1963)
gross144
hand0.1016 mhorses, 4 inches
hectare10 000 m2
hide~485000 m2120 acres (uncertain)
hogshead (beer)0.245 49 m354 UKgall
hogshead (claret)0.209 12 m3
hogshead (?)0.238 67 m3
horsepower ("Metric")735.50 W
horsepower (US & UK electrical)746 W
horsepower (US & UK mechanical)745.70 W
hour3600 s
hundredweight (UK)50.802 kg
inch0.0254 m
inch of mercury3386.39 Pa
inch of water249.09 Pa
inch-lbf0.113 Nmtorque
kilocalorie4186.8 J
kilogram force9.8067 N
kilowatt-hour3 600 000 J
knot (international)0.514 44.. ms-1
knot (UK)0.514 77 ms-1
league~5000 m
light-year9.4605e15 m
line0.002 116 66.. m17th century, 12 to the inch
litre-atmosphere101.33 J
maxwell1e-8 Wb
mil (US)2.54e-5 m0.001 inch
mile (old Irish)2048 m
mile (old Roman)1473 m
mile (old Scots)1807 m
mile (statute)1609.344 m5280 feet
mile per hour0.447 04 ms-1
millimetre of mercury133.322 Pa
millimetre of water9.8067 Pa
minim (UK capacity)5.9193e-8 m3
minute60 s
minute (arc)2.9089 rad
month (min)2 419 200 s
month (max)2 678 400 s
nautical mile (former)1853.99 m
nautical mile (international)1852 m
nautical mile (UK)1853.18 m6080 feet
nook~30000 m2quarter virgate
oersted79.577 47 Am-11/4pi * 1000
ounce apothecaries0.031 103 kg
ounce avoirdupois0.028 349 523 125 kg
ounce troy0.031 103 kg
parsec3.084e16 m
peck (UK capacity)0.009 092 2 m3
pennyweight0.001 555 2 kg24 grains
perch5.0292 m
perch (area)25.292 852 64 m2sq rod = 30.25 sq yds
pica4.233..e-3 mprinting type size (1/6 inch)
pin (beer)0.020 457 m336 UK pints
ping3.306 m2property size in Taiwan; 2 Japanese mats
pint (UK)5.6826e-4 m3
pint (US)4.7318e-4 m3
pole5.0292 m
poise0.1 Pa.sCGS viscosity
point3.5277..e-4 mprinting type size (1/72 inch)
pottle0.002 273 0 m3half UKgall
pound avoirdupois0.453 592 37 kgdefinition (in UK, Weights & Measures Act, 1963)
pound troy0.373 24 kg12 troy ounces
pound force4.4482 N
pound per square inch6894.76 Pa
poundal0.1382 N
quart (UK)0.001 136 5 m3
quart (US)9.4635e-4 m3
quarter (UK)12.701 kg28 lb
quintal (1)45.359 237 kg100 lb
quintal (2)100 kg
rod5.0292 m5.5 yds
rod (area)25.292 852 64 m230.25 sq yds, 160 to the acre
rood1011.714 105 6 m2quarter acre = 1210 sq yds
rotl0.448 kgancient Egyptian pound
second (arc)4.8481 rad
score20
scruple0.001 296 0 kg
slug14.594 kg
square foot0.092 903 04 m2
square inch6.4516e-4 m2
square mile2 589 988 m2
square yard0.836 127 36 m2
stère1 m3cut wood in France
stokes1e-4 m2s-1CGS kinematic viscosity
stone6.3503 kg14 lb (UK only, people only)
tablespoon1.5e-5 m3
tablespoon (US)1.4787e-5 m3
teaspoon5e-6 m3medicine bottles
teaspoon (US)4.9289e-6 m3
therm1.0551e8 J100 000 BTU
"thou" (UK)2.54e-5 m0.001 inch
tod12.7 kg28 lb (wool)
ton (UK)1016.046 908 8 kg2240 lb
ton (US)907.18 kg2000 lb
ton force (UK)9964.0 N
ton force (US)8896.4 N
ton of TNT4.184e9 Jbangs
ton of refrigeration3516.853 W
tonne1000 kg
torr101325/760 Pa1/760 of standard atmosphere
tun0.9456 m3(wine) 208 UKgall (13th century?)
tun1.1456 m3(wine) 252 UKgall
unit (electricity)3 600 000 Jkilowatt-hour
week604 800 s
virgate~121000 m230 acres
yard0.9144 mdefinition (in UK, Weights & Measures Act, 1963)
year (min)31 536 000 s
year (ave)31 556 952 s365.2425 days - Gregorian 400y ave
year (max)31 6224 00 s

List of material properties

References:

  1. The Shorter Oxford English Dictionary; 1993
  2. W Roger Breed; The Weights and Measures Act, 1963; Charles Knight; 1964
  3. The Chambers Dictionary; 1994
  4. Various correspondents on the US Metric Association mailing list
  5. Various physics textbooks
  6. Various history textbooks
  7. Wikipedia

nib 1997-02-23..2015-07-10

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