# On Systems of Units

In the post on “Fuel Costs of Point to Point Starship Travel”, our host expressed some frustration with Imperial units:

… they are in the screwball units of US\$ per million British Thermal Units (MBTU), where the British Thermal Unit is a quaint unit of energy defined as the heat input required to raise one pound of water by one degree Fahrenheit, which works out to somewhere between 1054 and 1060 joules in civilised units …

Please allow me to put that in context. Let’s start with what is a civilized Joule? One Joule (named after an Englishman) is a measure of the work done by a force of one Newton acting through a distance of one Meter. Clear now? If one is interested in how much heat can be produced from burning a given amount of hydrocarbons, obviously there is a need for a conversion factor from work to heat. Complications!

One of the interesting features of the Imperial system of units was that it was designed by humans for humans, with most units intended to allow people to have an intuitive feel for their size. For example, a yard (technically the distance from the king’s nose to his thumb) was approximately the length of a human stride. In contrast, the pointy-headed French intellectuals who defined the Meter originally intended a universality – it was to be one ten-millionth of the distance from the Earth’s equator to the pole along a meridian, a line of longitude. Why that rather strange one ten-millionth? Because that made their new Meter approximately equal to the old yard.

However, those French intellectuals made two mistakes, as described in Ken Alder’s “The Measure of All Things”, ISBN 0-7432-1675-X (2002). First, they erroneously assumed the world was round, and therfore all meridians would be the same length. In reality, the planet is an oblate spheroid, and thus their choice of measuring the meridian through Paris undermined their goal of universality. And then they made a simple arithmetic mistake. (Oops!). Thus, their new Meter was as arbitrary as the old Imperial yard.

An interesting point Alder makes in his book is that before the centralizers imposed the Meter, different units were used in different parts of France – mainly because the amount of land needed for a farm varied across the country due to differing soils, rainfall, & topography. A uniform Meter was convenient for the bureaucrats in distant Paris, but put a burden on the people who actually worked the land and paid the taxes.

Moving along, what is a Newton, named after the English scientist? One Newton is the force required to accelerate a mass of one Gram by one Meter per second per second. Oops! No, the mass to be accelerated is not a logical one Gram but rather one thousand Grams. In this supposedly-rational system of units, why is the base unit of mass one thousand Grams rather than one Gram? Oh look! A cute squirrel over there …

As I was saying, the Newton involves accelerating a mass of one thousand Grams at the rate of one Meter per second per second. If one holds a mass of one thousand Grams (the intellectuals called this a kiloGram) in one’s hand, one experiences a force from gravity of a rather non-intuitive 9.80665 Newtons. Contrast that with the intuitive Imperial units – the force of gravity on a mass of one Pound is … One Pound. The wise souls who devised the Imperial system included some rather subtle conversion factors in the background to enable that intuitive human result.

Another example of the Imperial system’s preference for intuitively-meaningful units is the Horsepower, originally defined by Scottish engineer James Watt for his steam engines, such that a one Horsepower engine delivered slightly more power than one good horse. (Excellent marketing technique!). In French “Systeme International” (SI) units, the comparable unit is named the Watt after him, defined as a power output of one Joule per second. It takes 746 Watts to equal 1 Horsepower – in intuitive terms, we might think of 1 Watt as being the not very useful 1 Hamsterpower.

This tendency of the rather awkward French-derived system to produce units which are neither intuitively meaningful nor usefully sized also appears in the unit for pressure – the Pascal, named after a Frenchman. Atmospheric pressure is 101,325 Pascals. Your tire pressure of a convenient 32 psi in the Imperial system becomes something in excess of 220,000 Pascals. This unit is so inconvenient that even the French turned their back on the SI system and instead adopted for most practical purposes the “Bar” – an unofficial unit equal to 100,000 Pascal. (Why 100,000? Do you really have to ask?) Of course, that makes your tire pressure an inconvenient 2.18 “Bar” – good luck getting those tire pressures balanced!

Strangely, those intellectuals never got round to defining an SI unit of volume. Instead of the physically obvious 1 Barrel of oil, they demand the use of 0.15899 cubic Meters. Exasperated French people tried to plug this hole by inventing another unofficial unit, the “Litre”, equal to one cubic deciMeter. At least it is easier for the European motorist to buy a “Litre” of fuel for his automobile rather than 0.001 cubic Meters.

Even the proponents of French units recognize their limits. When dealing with the very small, it is more convenient to think about the size of a methane molecule as 3.8 (non-SI) “Angstroms” than as 0.38 nanoMeters. When dealing with the cosmologically large, 1 (non-SI) “Light-Year” is intuitively more understandable than 9.46 petaMeters. The creators of a set of units have to choose between developing a system which has convenient understandable human scales or developing an internally-consistent rational system. The pointy-headed French intellectuals turned their backs on the human scale and aimed for rationality – but missed.

Any system of units is really a language. It facilitates communication among those who speak that language while being confusing to those who don’t. Some have argued that English-speakers should instead learn & use the more precise Russian language because English is so riddled with ambiguities. However, those of us who speak English manage to get by, and would be reluctant to give up Shakespeare for a reduction in occasional ambiguities.

The adoption of SI units was driven by the same idealistic multi-nationalism that gave us the League of Nations, the United Nations, and the European Union. In principle, such centralized systems should be better than what went before – but reality has shown us something different. This reliance on changeable bureaucratic consensus points to the Achilles’ Heel of the Systeme International in today’s world – the undeniable fact that most units are named after straight white male Europeans, with not a transgendered single mother of color in sight. Fortunately, the Usual Suspects are mostly technically-illiterate and so far have paid little attention to the SI’s blatant demonstration of sexism, racism, & homophobia. However, it is inevitable that, at some point in the future, the users of the SI units will find themselves compelled to talk about Kardashians instead of Joules and Malcolm Xs instead of Watts. You know it is coming!

6 Likes

Consider the humble “pint”:

• Imperial pint: 568.26125 millilitres
• U.S. liquid pint: 473.176473 millilitres
• U.S. dry pint: 550.6104713575 millilitres
• India “pint bottle”: 330 millilitres
• South Australian pint: 425 millilitres
• Australian pint: 570 millilitres

One US liquid pint of water weighs 1.04318 pounds (16.69081 ounces), which gives rise to a popular saying: “A pint’s a pound, the world around”.

However, the statement does not hold around the world because the British imperial pint, which was also the standard measure in Australia, India, Malaya, New Zealand, South Africa and other former British colonies, weighs 1.2528 pounds, giving the origin of a popular saying used in Commonwealth countries: “a pint of pure water weighs a pound and a quarter”.

2 Likes

Meh. I’m with Gavin. I use U.S. traditional units wherever I’m allowed. (I’m an engineer, so not always allowed.) I really don’t care that there are deviations with the former British Imperials. I do care that most mental operations on them are doubling or halving. People are pretty good at that, and don’t even realize they are using binary fractions.

1 Like

Yes. Personal view is that engineers & technical people should be “multi-lingual”, at least when it comes to systems of units. The point about a practical unit is that it should be conveniently sized for its purpose, both in its magnitude and its sensitivity. Cups & tablespoons are convenient measures in the kitchen. Fathoms work well for nautical charts. The Richter scale is appropriate for earthquakes.

One of the silliest examples of “mono-lingualism” I have seen was a giant computer simulation program written strictly in terms of SI units – rejecting even the metric units which are an attempt to bend the SI system closer to reality. Time was measured in the SI unit of seconds. Simulations were modeling processes which took half a century. The engineer shakes his head.

1 Like

Imperial units are a huge PITA. What’s your mass in slugs? I bet you have no idea.

The main thing that SI units have going for them is their decimal nature. Calculations and conversions are a heck of a lot simpler in such a system than in one that has 63,360 inches to the mile or 640 acres in a square mile.

Science uses orders of magnitude, as do SI units. There’s a reason that the scientific community around the world (yes, even in the U.S. of A.) ditched imperial units many decades ago. The only reason I know about slugs, poundals, and furlongs is that they made for good jokes in school. Personally, I favor the Smoot as the base unit of length but it’s unlikely to be adopted.

The point is, it doesn’t matter where the base units come from. What counts is the relations among them. I don’t care that the Frogs didn’t know the Earth was a spheroid. It’s irrelevant to the way the units are used. I’d rather be able to convert centimeters to kilometers without a calculator, which is tough to do with inches and miles.

Hey, if you prefer feet to meters because one foot is about the length of your foot, that’s cool. I like that too. But as soon as I can, I convert those whackadoodle units into something that’s easier to work with. And I know all my get-out-of-imperial units conversions by heart. All you gotta know for length is one inch equals 2.54 cm exactly.

3 Likes

I neither know nor care. That’s the point.

Yes, that one is handy.

This points one one of the many sloppy aspects of U.S. conventional units: the confusion between mass and force, which you’d hardly expect from a system that traces its origin to the land of Newton. In SI, the unit of mass is kilogram, while the unit of force is (appropriately) the newton. In U.S. units, both mass and force are called “pounds”, in most cases distinguished in meaning only by context, although when both are used together, they write “pound-force”. What’s a pound-force? Well, it’s the gravitational force exerted by a mass of one pound-mass under the so-called “standard acceleration due to gravity” which is defined as the acceleration due to gravity by an object in vacuum near the Earth, which in U.S. units is defined precisely as the easily-remembered 32.17405 foot/sec². But this is just a made-up convention: the actual gravitational acceleration at Earth’s surface varies by around 0.5% depending upon latitude, altitude, and local geology. So, they start by confusingly using the same unit for mass and force, requiring a distinguishing suffix, then they define force by bringing in another “constant” which is not defined in terms of the fundamental units but parochial to the Earth, but actually varies from location to location on the Earth to such a degree that it was known to be sufficiently imprecise for precision measurements since the 18th century.

If that weren’t enough, we have another unit of mass, the slug, equal to 32.174049 pounds-mass, which is the mass that one pound-force causes to accelerate at a rate of 1 foot/sec². Oh, and there’s the poundal, an alternative unit of force defined as the force required to accelerate one poud-mass at 1 foot/sec². So whacked-out was the confusion between pound-mass and pound-force that in my first year mechanics class at engineering school, the professor, who insisted on using U.S. units for everything, made us calculate using slugs and poundals. The physics department thought this very funny, and considered there was no further need to explain or justify their preference for SI units in calculations.

And let’s not even get into the distinction between “foot-pound” (a unit of energy with SI equivalent joule) and “pound-foot” (unit of torque, SI newton metre).

2 Likes

Let’s not miss the point – all known systems of units are arbitrary and have limitations. What is important is to use units which are appropriate to the task at hand. No system today is “Fit for All Purposes” – including SI units. The cubic Meter is not a useful volume unit for buying milk. While the nanoMeter is a useful unit for measuring traces on integrated circuits, no-one would ever have any need to convert 7 nanoMeters into kiloMeters.

The human race has performed amazing feats using Imperial units, from the Forth Rail Bridge to the Boeing 747 to the Moon Landings. The human race has also been able to build major projects using SI units – China’s High Speed Rail network comes to mind. Just as humans have been able to produce great literature in English as well as in Russian. Technologists need to be multi-lingual in units.

Every time we see something quoted in litres or bars, we simply should remember that the SI system has its limitations as well as its advantages – same as the Imperial system. Now, about those ergs.

3 Likes

Actually, you should care since you like “U.S. traditional units” and the slug is the measure of mass in that system. I expect most engineers know that, at least the MEs anyhow. On the other hand, maybe they don’t anymore. Are they still teaching those units in US engineering schools?

1 Like

No, but they might need to convert feet, or even inches, to miles. I promise it’s easier to convert cm to km.

Metaphorically speaking, people have voted with their feet. (Get it?) The world overwhelmingly chose SI in spite of the sun once never having set on the British Empire. They didn’t do it because the French Revolution was so great; they did it because it’s easier to use.

And, btw, the liter was a unit in SI’s predecessor system from the very beginning. There were always units specifically for area and volume, just as they are in the Imperial System. Just as no one would sell milk by the cubic foot, no one would ever suggest it be sold by the cubic meter. Likewise, farmland is not specified in square feet. That’s why liters and hectares exist, parallel to quarts and acres.

For those who like quirky units, you might want to consider the FFF system (furlong–firkin–fortnight). Unfortunately, it substitutes the furlong for the far more intuitive Smoot. Thus inspired, I’m going off to cycle a hundred or so furlongs over the next few millifortnights.

2 Likes

Lest we forget, remember this expensive translation failure? From SIMSCALE:

The Mars Climate Orbiter, built at a cost of \$125 million, was a 338-kilogram robotic space probe launched by NASA on December 11, 1998 to study the Martian climate, Martian atmosphere, and surface changes. In addition, its function was to act as the communications relay in the Mars Surveyor ‘98 program for the Mars Polar Lander. The navigation team at the Jet Propulsion Laboratory (JPL) used the metric system of millimeters and meters in its calculations, while Lockheed Martin Astronautics in Denver, Colorado, which designed and built the spacecraft, provided crucial acceleration data in the English system of inches, feet, and pounds. JPL engineers did not take into consideration that the units had been converted, i.e., the acceleration readings measured in English units of pound-seconds^2 for a metric measure of force called newton-seconds^2. In a sense, the spacecraft was lost in translation.

2 Likes

I think there is a misunderstanding here as to what the SI units system is all about and how it is used. The purpose of SI is to define a set (of seven) orthogonal units, all defined in terms of fundamental physical properties which could be, in practice, determined anywhere in the universe at any time by anybody, given the definition and the ability to understand what it meant.

This does not mean that only these “SI base units” are to be used in expressing measures, and nobody uses them that way. When working with measurements in various fields, one chooses derived units, defined in terms of the SI base units, which are appropriate for the application. When working with wavelengths of visible light, one typically uses nanometres. When measuring liquids, litres (0.001 metre³) makes sense, or millilitres for small quantities. Astronomers use astronomical units, defined as 149,597,870,700 metres, and particle physicists express energy as electronvolts, 1.602176634×10^{−19} joules. Many units for other physical quantities can be defined as the product of base units, for example the volt is defined as (kg m²)/(sec³ ampere). The point is that the definition of the unit employed is always referenced back to the SI base units and can be easily converted through them as necessary. Because the definitions of the SI units are in terms of fundamental constants such as the speed of light, Planck’s constant, and the charge of the electron, as improved instrumentation and measurement techniques permit determining these values more accurately in the future, all of the units referenced to SI gain accuracy automatically.

As the U.S. customary units have been, since 1959 (and in large part since 1893), defined in terms of SI units or their metric predecessors, with exactly defined conversion factors, they can be considered as simply another alternative set of definitions based upon SI. When the SI kilogram was redefined in 2019 based upon Planck’s constant, the second, and the metre, that improved and more stable definition automatically became the definition of the U.S. pound(-mass).

2 Likes

Hello, allow me to point out several errors in your relation of the historical facts and in your explanation of these facts.

Jean-Baptiste Delambre and Pierre Méchain can certainly not be qualified as intellectuals, on the one hand because this word did not exist in their time, nor even the underlying concept, and on the other hand because a simple consultation of reference books would have taught you that the first was a mathematician, astronomer, historian of astronomy, and geodesist, and the second an astronomer and surveyor, which is a long way from the Parisian intellectuals that you describe, in any unit used to measure that way.

Also the argument of having to link a measurement system to the objects that one measures is absurd. Because these objects disappear, evolve, are not the same in each country. The average length of a human foot in the 16th century is not the same as the average length of a foot today. This is of no use, except to make everyone laugh as it has been said elsewhere in this discussion.

The obvious thing to do was to invent a system of measurement independent of cultures and habits, which was done by choosing the only thing that all human beings share, the Earth.

On the other hand, it has been known for a long time that the Earth was not perfectly spherical, at least since Picard in 1671, who argued that the Earth was not perfectly spherical, then Newton, then Huygens in 1690.

The reason for the choice of the terrestrial meridian was not its regularity, but a historical and cultural reason: Their hope: to see all the men of the world using the globe as a common standard of measurement. Their goal: to define precisely the length of the meter, fixed at the ten millionth part of the quarter of the terrestrial meridian, according to the scientists of the Academy. The meter would be eternal because it would be drawn from the Earth, itself eternal, without any reference to human interests. It would be independent of any social negotiation and of any temporal change. And it would belong equally to all the men of the Earth, as the Earth belonged equally to all of them.
We can say that they were right, except for a small country at the time, the USA, which for some reason clung to its ancient history and still clings to it a little (without conviction and sometimes with bad faith).

3 Likes

Not only that, but the goal has long been to move away from physical objects for what I hope are obvious reasons. It’s been well over 50 years since the standard meter, kept in a vault in a suburb of Paris, was abandoned in favor replicable measurements of fundamental physical processes. The time unit second was next to fall, if memory serves. The last was the kilogram, as noted above. Now we don’t have to worry about the corrosion or other decay of a chunk of platinum-iridium in a French vault.

3 Likes

As science enthusiasts, we understand the measurement system we use is relatively easy to adapt to, be it American (aka Imperial), Metric (aka S.I.) or other. I think it is best to use the one your reader/audience is comfortable with.

Due to “Common Core” math in the U.S., it saddens me that a generation of Americans will not have the intuition with math and measurement as we have.

But the growing number of home-schooled students gives me much hope.

4 Likes

To get serious for a moment – Would that that were so! Instead, too often we see “SI Purists” trying to use very inconveniently-sized SI units instead of something more practical. In my field, Pascal-abuse is most common. All I am suggesting is – Let’s be sensible, like engineers should be; use the appropriate tool for the task.

You make a good point that Imperial units are now defined in terms of the same fundamental constants as SI units. The logical corollary is that there are now no “quaint” units, simply unfamiliar units designed to be suitable for specific tasks.

Some time ago, I had a conversation with an old Brit. He complained that young Brit shop assistants could barely make change, even though they had a modern till telling them exactly what change to give. In the Good Old Days, he said, shop girls (usually female then) would calculate the change in their heads – and almost always get it right. And that was pre-decimalization, when they had to deal with Pounds, Shillings, and Pence (12 pennies to the shilling, 20 shillings to the pound, and odd coins like the half-crown).

Is it possible that one of the unintended consequences of moving to simplified calculations (whether for currency or units) has been to dumb us all down? Just like an athlete needs to keep in training, maybe our brains need the exercise of calculations which involve more than moving a decimal point? Just speculating here.

4 Likes

Nah. The causality runs the other way: people are getting dumber and everything has to be dumbed down to accommodate that ugly reality.

2 Likes

Come on man. The most popular grade at the most prestigious institutions is now A-. That giving everyone a trophy worked.

2 Likes

It isn’t just pounds, gallons, feet, Fahrenheit degrees, screw threads, and paper sizes. Did you know that there are different rules of chess [PDF] in the U.S. and everywhere else in the world?

3 Likes