Metrology for Americans - or why a pint is not a pound the whole world round

[bilby]

Not just for Americans - this is for anyone who measures stuff, and cares about getting it right, rather than 'mostly right' or 'nearly right'.

First some basic principles:

SI, or GTFO.

- SI is the only measurement system you need. If you know what a BTU is, forget it. If you care what a BTU is, stop it. You are making things needlessly complex.
- Inches, Pounds, Feet, Miles, Horsepower etc. etc. are great, if you live in the middle ages. You don't live in the middle ages. Stop using them.​

Units of measure matter. They are as important as the numbers to which they are attached, and should be treated with the same respect.

- Don't do sums with the numbers, and then guess the appropriate units for the result; do the same mathematical operations on the units, and you will get the right unit in the result automatically.​

Units of measure are algebraic terms. They are treated exactly the same way as the numbers when using equations.

- So an object that moves 100m in 20s is NOT going at 100/20 = 5; it is going at 100m/20s = 5m/s​

This is important. For a given value of 'important'.

- You don't have to follow these rules; but if you ignore them, it's your own fault when your expensive space probe crashes into Mars.​

Simplifying assumptions are OK. As long as you are aware that you are making them, and what they are - and as long as you tell everyone else, so they are aware too.

- Assuming a temperature of 273K and a pressure of 100kPa, a 1l of water has a mass of approximately 1kg. This does not make it acceptable to assume that 1l = 1kg under any other circumstances, nor to assume that the relationship is exactly 1:1 even under these exact circumstances. ​

Having got that out of the way, there are three major elements to a measurement system; Dimensions, Basic Units, and Derived Units.

Dimensions:

A dimension is a measurable that cannot be described as a combination of other measurables. There are fewer of them than you might imagine. The most commonly encountered are:

Length (L) - the distance between two points in space
Time (T) - the distance between two points in time
Mass (M) - the strength with which an object interacts with gravitational fields
Charge (Q) - the strength with which an object interacts with electromagnetic fields

Basic Units:

A Basic unit is the unit used to measure a dimension:

Metre (m) - the unit of Length
Second (s) - the unit of Time
Kilogram (kg) - the unit of Mass
Coulomb (C) - the unit of charge

Derived Units:

A Derived unit is a unit made up from a combination of Basic units, that is useful for a particular type of measurement. A few examples include*:

Speed - Rate of change of Length over Time (L.T ^-1). Measured in metres per second (m.s^-1).
Acceleration - Rate of change of Speed over time (L.T ^-2). Measured in metres per second per second (m.s^-2).
Force - The acceleration of a mass (M.L/T²). Measured in Newtons (N). N = kg.m.s^-2. Weight is a special case of Force; Weight is the force acting on a mass due to the acceleration of gravity.
Energy - The ability to do work (for example to accelerate a mass) (M.L².T ^-2). Measured in Joules (J). J = N.m = kg.m².s^-2
Power - Energy applied over time (M.L².T ^-3). Measured in Watts (W). W = J.s^-1 = kg.m².s^-3
Frequency - Events per second (T ^-1). Measured in Hertz (Hz)**. Hz = s^-1
Pressure - The force applied to an area (M.L^-3) Measured in Pascals (Pa). Pa = N.m^-2 = kg.m^-1.s^-2.

In the SI system, all of these derived units are defined with a 1:1 relationship to the basic units. This makes calculations between different measurements supremely easy, as there are no conversion factors to include.

When dealing with real measures, it is common to need very large or very small numbers; so SI includes a set of prefixes that denote multiples of 10³; the most common of which are:

T - Tera- 10¹²
G - Giga- 10⁹
M - Mega- 10⁶
k - Kilo- 10³ (NB the use of a lower case 'k' for this prefix is mandatory, to avoid confusion with Kelvin, the measure of absolute temperature)
m - Milli- 10^-3
μ - Micro- 10^-6 (NB this is sometimes rendered as 'u' due to the absence of a 'μ' character)
n - Nano- 10^-9

So:

1TJ = 1,000,000,000,000J = one million million Joules
1nm = 1/1,000,000,000m = on thousand millionth of a metre

The prefixes 'hecto-', 'deca-', 'deci-' and 'centi-'; denoting 10², 10, 10^-1 and 10^-2 respectively belong to the obsolete 'metric' system that was a precursor to SI, and should be avoided. Hence a length of 5cm should instead be rendered as either 0.05m, or as 50mm.

[/braindump]






*I have not listed any of the various electromagnetic derived units here, because I am too lazy. A brief list of the main ones can be found on Wikipedia if you are interested.

**In nuclear physics, when measuring radioactive decay, events per second are often measured in Becquerels (Bq) rather than Hertz (Hz). The two units have the same value (s^-1)

 

[beero1000]

It's funny that the base unit for mass is the kilogram and not the gram.

According to the BIPM:

The reason why "kilogram" is the name of a base unit of the SI is an artefact of history.

Louis XVI charged a group of savants to develop a new system of measurement. Their work laid the foundation for the "decimal metric system", which has evolved into the modern SI. The original idea of the king's commission (which included such notables as Lavoisier) was to create a unit of mass that would be known as the "grave". By definition it would be the mass of a litre of water at the ice point (i.e. essentially 1 kg). The definition was to be embodied in an artefact mass standard.


After the Revolution, the new Republican government took over the idea of the metric system but made some significant changes. For example, since many mass measurements of the time concerned masses much smaller than the kilogram, they decided that the unit of mass should be the "gramme". However, since a one-gramme standard would have been difficult to use as well as to establish, they also decided that the new definition should be embodied in a one-kilogramme artefact. This artefact became known as the "kilogram of the archives". By 1875 the unit of mass had been redefined as the "kilogram", embodied by a new artefact whose mass was essentially the same as the kilogram of the archives.


The decision of the Republican government may have been politically motivated; after all, these were the same people who condemned Lavoisier to the guillotine. In any case, we are now stuck with the infelicity of a base unit whose name has a "prefix".

 

[skepticalbip]

It's funny that the base unit for mass is the kilogram and not the gram.

The gram is the base unit for mass in the CGS system.. but that would make it funny that the centimeter was used as the base unit for length.

 

[bilby]

It's funny that the base unit for mass is the kilogram and not the gram.

The gram is the base unit for mass in the CGS system.. but that would make it funny that the centimeter was used as the base unit for length.

I believe the cgs system was intended to make people feel less bad about not using the inch, by providing an alternate unit of length that still fits nicely in the hand. A mm is a bit too small, and a m is rather too large. On the other hand, the kg is a nice size to hold, while the g is rather small. A kg bag of rice, sugar or flour feels about right to carry, but a g is just a pinch of dust in the palm of your hand.

Still, anything is better than using a unit like the pound, where you have to further explain if you are discussing force or mass; or the pint, where you have to explain if you are using the US or UK standard - made even more confusing by the 'A pint's a pound the whole world round' mnemonic, which is a viscious lie, as a pint's only a pound in the 5% of the world's land area occupied by the USA. A pint's a pound and a quarter in 95% of the world. But only if it is a pint of water, at standard temperature and pressure, of course. It wouldn't do to make things simple

 

[skepticalbip]

The gram is the base unit for mass in the CGS system.. but that would make it funny that the centimeter was used as the base unit for length.

I believe the cgs system was intended to make people feel less bad about not using the inch, by providing an alternate unit of length that still fits nicely in the hand. A mm is a bit too small, and a m is rather too large. On the other hand, the kg is a nice size to hold, while the g is rather small. A kg bag of rice, sugar or flour feels about right to carry, but a g is just a pinch of dust in the palm of your hand.

Still, anything is better than using a unit like the pound, where you have to further explain if you are discussing force or mass; or the pint, where you have to explain if you are using the US or UK standard - made even more confusing by the 'A pint's a pound the whole world round' mnemonic, which is a viscious lie, as a pint's only a pound in the 5% of the world's land area occupied by the USA. A pint's a pound and a quarter in 95% of the world. But only if it is a pint of water, at standard temperature and pressure, of course. It wouldn't do to make things simple

I like your OP. It reminds me of a physics professor I once had. He posed his questions in his unique furlong-stone-fortnight system and required the answers be in metric units. The object was to drill us to always include the units along with the numbers when doing calculations and to understand conversions.
.

 

[Bomb#20]

It's funny that the base unit for mass is the kilogram and not the gram.

The gram is the base unit for mass in the CGS system.. but that would make it funny that the centimeter was used as the base unit for length.

Well, there's no meter-gram-second system, so we can't get away from adding arbitrary constants to our exponents*, so we might as well at least get rid of the arbitrary conversion factors that aren't powers of ten. The way to do that is to abolish the meter. We should measure time in nanoseconds and distance in feet.

(* For some reason, nobody at work was willing to go for the obvious natural metric unit of chip real estate, the attare. )

 

[skepticalbip]

The gram is the base unit for mass in the CGS system.. but that would make it funny that the centimeter was used as the base unit for length.

Well, there's no meter-gram-second system, so we can't get away from adding arbitrary constants to our exponents*, so we might as well at least get rid of the arbitrary conversion factors that aren't powers of ten. The way to do that is to abolish the meter. We should measure time in nanoseconds and distance in feet.

(* For some reason, nobody at work was willing to go for the obvious natural metric unit of chip real estate, the attare. )

Yeah, I have considered the measurement system mess. I see only two solutions, either rename the decimeter as the new meter (the current meter would become a decameter) and rename the kilogram as the new gram so have a new MGS system that makes sense (a cubic new meter will be a liter and a liter of water will be approx. one gram) or scrap metric systems and adapt my old physics prof's unique furlong-stone-fortnight system as the new international system of measurements.

 

[Bomb#20]

Yeah, I have considered the measurement system mess. I see only two solutions, either rename the decimeter as the new meter (the current meter would become a decameter) and rename the kilogram as the new gram so have a new MGS system that makes sense (a cubic new meter will be a liter and a liter of water will be approx. one gram)

Per the OP, we're supposed to be getting this right, not just nearly right. So can we quit using water for measurement already? What the heck is "water"? How the heck is the lab next to yours supposed to know what substance you used when you supposedly measured the density of "water"? If we're going to define mass by a quantity of a substance it should be a cubic new meter of gold.

or scrap metric systems and adapt my old physics prof's unique furlong-stone-fortnight system as the new international system of measurements.

"Stone"? Heretic! Mass is measured in firkins of beer!

 

[fromderinside]

Bah. Humbug. I'm trying to convert this spec for thrust written as Poundels in slugs per parsec per fortnight squared into newtons in kilograms per angstrom per light year squared.

Got Milk?

 

[bilby]

Per the OP, we're supposed to be getting this right, not just nearly right. So can we quit using water for measurement already? What the heck is "water"? How the heck is the lab next to yours supposed to know what substance you used when you supposedly measured the density of "water"? If we're going to define mass by a quantity of a substance it should be a cubic new meter of gold.

None of the basic units of measure are defined in terms of water, nor have they been since 1798.

The kg is defined as the mass of a Platinum master called the IPK (International Prototype Kilogram). Until the recent spike in the gold price, it was worth more (as scrap metal) than a kg of gold. A litre of water at 4^oC and 100kPa has a mass a little greater than 1kg, due to the improvement in measuring precision since the IPK was made. However, the precise volume of the litre is not known.

The litre is defined as 10^-3m³, but the metre has an unknown length. This is because the second and the speed of light in a vacuum are precisely defined; so you cannot attempt to more accurately measure the speed of light, but must instead attempt to more accurately measure the length of a metre.

 

[barbos]

well, originally kilogram was defined using water. And it's very convenient.

 

[Jokodo]

Per the OP, we're supposed to be getting this right, not just nearly right. So can we quit using water for measurement already? What the heck is "water"? How the heck is the lab next to yours supposed to know what substance you used when you supposedly measured the density of "water"? If we're going to define mass by a quantity of a substance it should be a cubic new meter of gold.

Why on the earth (or in the universe) would you use gold? It's not the densest metal (that'd be osmium) and certainly not the lightest, it's not the rarest (iridium among the stable elements in the earth's crust, I haven't found any universe-wide statistics) and far from the most abundant. There really isn't anything special about gold, objectively. Water at least is the most abundant multi-element molecule in the universe, so it has more going for it than gold.

And what's the thing about room temperature anyway? Isn't that just shorthand for "temperature at which monkeys feel comfortable"?

If we really want our measurement system to reflect the basic fabric of the universe, our unit of mass should be based on a cubic <basic_unit_of_length> of hydrogen at the temperature and pressure where fusion initiates.

 

[Bomb#20]

Per the OP, we're supposed to be getting this right, not just nearly right. So can we quit using water for measurement already? What the heck is "water"? How the heck is the lab next to yours supposed to know what substance you used when you supposedly measured the density of "water"? If we're going to define mass by a quantity of a substance it should be a cubic new meter of gold.

None of the basic units of measure are defined in terms of water, nor have they been since 1798.

The kg is defined as the mass of a Platinum master called the IPK (International Prototype Kilogram).

True, but the mass of the platinum master was chosen to match a liter of water. In any event, platinum is just as bad a material for this as water -- you can't ever get samples with repeatable composition. (Besides which, the IPK isn't even platinum -- it's about 10% iridium, which means god knows how much of each is really in it.)

Until the recent spike in the gold price, it was worth more (as scrap metal) than a kg of gold.

Another point in gold's favor.

A litre of water at 4^oC and 100kPa has a mass a little greater than 1kg, due to the improvement in measuring precision since the IPK was made. However, the precise volume of the litre is not known.

If you want precision, weighing an artifact is a nutty way to go -- you might as well define the second as the ticking rate of a specific clock in a Paris basement that you bring out every forty years to compare with other clocks. The way to define mass as precisely as N periods of cesium radiation is to define it as the mass of N atoms of type X. The obvious choice for N and X is the number of gold atoms in a cube of the standard length.

The litre is defined as 10^-3m³, but the metre has an unknown length. This is because the second and the speed of light in a vacuum are precisely defined; so you cannot attempt to more accurately measure the speed of light, but must instead attempt to more accurately measure the length of a metre.

Well that could be a problem. So how much is the current uncertainty in the length of a decimeter, compared to atomic spacing in crystals?

Why on the earth (or in the universe) would you use gold? It's not the densest metal (that'd be osmium) and certainly not the lightest, it's not the rarest (iridium among the stable elements in the earth's crust, I haven't found any universe-wide statistics) and far from the most abundant. There really isn't anything special about gold, objectively. Water at least is the most abundant multi-element molecule in the universe, so it has more going for it than gold.

Why would we want high density? Rarity is undesirable -- scandium wouldn't be a bad choice but it's a lot more expensive than gold. What the heck is "water"? An uncertain and irreproducible mixture of H₂O, H₂¹⁸O, HDO, D₂O, OH+ and god knows what all else.

If we really want our measurement system to reflect the basic fabric of the universe, our unit of mass should be based on a cubic <basic_unit_of_length> of hydrogen at the temperature and pressure where fusion initiates.

Great. Now my mass unit is heavier than yours because by source of hydrogen has more deuterium than yours. Thanks a lot!

I suppose we could get away with using terbium -- that's quite a bit cheaper than gold. Calculating exactly how many terbium atoms fit in a cube <basic_unit_of_length> on a side would be more involved than the same calculation for gold -- gold has that lovely face-centered-cubic crystal structure that makes it especially convenient for this purpose. Terbium crystals are full of hexagons; but it's no doubt manageable.

 

[Underseer]

The metric system is part of the vast international science conspiracy to convince us of anthropogenic climate change! Don't fall for it, or else FEMA will invade your state and put you all into reeducation camps just like they're doing in Texas right now! Freedom isn't free! [/conservolibertarian]

 

[Jokodo]

None of the basic units of measure are defined in terms of water, nor have they been since 1798.

The kg is defined as the mass of a Platinum master called the IPK (International Prototype Kilogram).

True, but the mass of the platinum master was chosen to match a liter of water. In any event, platinum is just as bad a material for this as water -- you can't ever get samples with repeatable composition. (Besides which, the IPK isn't even platinum -- it's about 10% iridium, which means god knows how much of each is really in it.)

Until the recent spike in the gold price, it was worth more (as scrap metal) than a kg of gold.

Another point in gold's favor.

A litre of water at 4^oC and 100kPa has a mass a little greater than 1kg, due to the improvement in measuring precision since the IPK was made. However, the precise volume of the litre is not known.

If you want precision, weighing an artifact is a nutty way to go -- you might as well define the second as the ticking rate of a specific clock in a Paris basement that you bring out every forty years to compare with other clocks. The way to define mass as precisely as N periods of cesium radiation is to define it as the mass of N atoms of type X. The obvious choice for N and X is the number of gold atoms in a cube of the standard length.

The litre is defined as 10^-3m³, but the metre has an unknown length. This is because the second and the speed of light in a vacuum are precisely defined; so you cannot attempt to more accurately measure the speed of light, but must instead attempt to more accurately measure the length of a metre.

Well that could be a problem. So how much is the current uncertainty in the length of a decimeter, compared to atomic spacing in crystals?

Why on the earth (or in the universe) would you use gold? It's not the densest metal (that'd be osmium) and certainly not the lightest, it's not the rarest (iridium among the stable elements in the earth's crust, I haven't found any universe-wide statistics) and far from the most abundant. There really isn't anything special about gold, objectively. Water at least is the most abundant multi-element molecule in the universe, so it has more going for it than gold.

Why would we want high density?

I don't know, you're the one who brought up gold, commonly known as one of the densest elements. In fact, being the densest monoisotopic (and mononuclidic) element appears to be the only distinction gold holds.

Rarity is undesirable -- scandium wouldn't be a bad choice but it's a lot more expensive than gold.

Because it's mononuclidic? If rarity is undesirable and density isn't what you want to go for either, maybe we should take beryllium, fluor, sodium or aluminium - all of which are monoisotopic and much more frequent than either scandium or gold?

What the heck is "water"? An uncertain and irreproducible mixture of H₂O, H₂¹⁸O, HDO, D₂O, OH+ and god knows what all else.

If we really want our measurement system to reflect the basic fabric of the universe, our unit of mass should be based on a cubic <basic_unit_of_length> of hydrogen at the temperature and pressure where fusion initiates.

Great. Now my mass unit is heavier than yours because by source of hydrogen has more deuterium than yours. Thanks a lot!

I suppose we could get away with using terbium -- that's quite a bit cheaper than gold. Calculating exactly how many terbium atoms fit in a cube <basic_unit_of_length> on a side would be more involved than the same calculation for gold -- gold has that lovely face-centered-cubic crystal structure that makes it especially convenient for this purpose. Terbium crystals are full of hexagons; but it's no doubt manageable.

Sodium and aluminium too have cubic crystal structure. Still no reason to pick gold.

 

[Jokodo]

Also, Bomb, you haven't even stated at which temperature and pressure. It's not like gold has an unusually low coefficient of thermal expansion so you could just ignore that. If you consider cubic crystal structure an important feature and a low coefficient of thermal expansion a relevant bonus, niobium should be your material of choice. I really cannot concern any objective reason to pick gold.

 

[Eldarion Lathria]

I Once Had a Professor Who talked about Leagues

I like your OP. It reminds me of a physics professor I once had. He posed his questions in his unique furlong-stone-fortnight system and required the answers be in metric units. The object was to drill us to always include the units along with the numbers when doing calculations and to understand conversions.
.

We asked him if it was a nautical league, a royal league, a Spanish gunner's league, an Imperial German League or a Dutch League he was talking about. That broke him of the habit.

Eldarion Lathria

 

[Bomb#20]

Because it's mononuclidic? If rarity is undesirable and density isn't what you want to go for either, maybe we should take beryllium, fluor, sodium or aluminium - all of which are monoisotopic and much more frequent than either scandium or gold?

Hmm, yes, a standard weight made of fluorine. Why didn't I think of that? All those elements are pretty reactive -- they even use aluminum for rocket fuel. That seems like an undesirable characteristic in an object you want to remain the same for years and years.

Also, Bomb, you haven't even stated at which temperature and pressure.

I'm pretty sure we can pick a temperature and pressure at which gold is a solid that's repeatable with more precision than the temperature and pressure where hydrogen fusion initiates.

It's not like gold has an unusually low coefficient of thermal expansion so you could just ignore that. If you consider cubic crystal structure an important feature and a low coefficient of thermal expansion a relevant bonus, niobium should be your material of choice. I really cannot concern any objective reason to pick gold.

Actually, on paper niobium looks like an excellent choice. I didn't consider it because it wasn't on Wikipedia's list of elements used for metrology, so I assume it must have a downside; they don't explain further. But I know it forms a passivation layer in the presence of oxygen; if that's severe enough it would throw off the mass of your standard object.

By the way, is this about your visceral reaction against a gold standard?

 

[Jokodo]

By the way, is this about your visceral reaction against a gold standard?

To the contrary, it's all about your desperate attempts to make out gold as somehow objectively special when it clearly isn't.

 

[skepticalbip]

I think people get too worked up over their preferred measurement system. The system used is irrelevant as long as the one someone has chosen is standardized and they are able to convert measurements to those other silly systems that other people prefer. The only real important thing about a measurement system is that everyone know and agree on the value of the standards used.

The value of a measurement system is in its usefulness. The SAE system is useful because it makes everyday estimates of approximate measurement values easy without a ruler because many are based on average body measurements, so it’s handy for an individual’s shopping when exactness and critical measurement are not required. The metric system is useful for people who find it difficult to multiply or divide by anything other than ten or multiples of ten.