By The Metric Maven

Bulldog Edition

I’ve always liked wood. My Grandfather was a carpenter, my father also knows how to work with wood. I, alas, do not. My father can generally recognize different woods, I haven’t a clue. The variety of woods that exist is astonishing. I recall reading about how the English carpenter and clockmaker John Harrison (1693-1776), used a wood called Lignum vitae, to construct wooden clocks. This wood actually has the property that is is self-lubricating, which allowed Harrison to make bearings and gears of it for his pendulum clocks. It is also one of the hardest woods in nature. In my youth I marveled at the Balsa wood rubber band driven airplanes available at the local dime store. I also have an interest in photographing wooden grave markers. An image of one of these “tombstones” I photographed is shown in the photo above.

I thought back on all this when paging through an old book called *Science in Everyday Things* by Engineer William C. Vergara and published in 1958. The book is a list of questions with answers, and one of them is: “Does all wood float?” What I assume he means is that given a solid cube of wood, will it float in water? When Vergara offers his answer, he informs his readers that the density of water is 62.5 pounds per cubic foot. Any wood with a density above this will sink and any below this will float. What struck me was the contrived and arbitrary nature of this value. It reminds me of the freezing point of water being defined as 32 degrees, an arbitrary magic number to be remembered on the Fahrenheit scale, because of poor measurement planning.

What struck me even more was that I was still going along with all the people who use kilograms per meter cubed. In my view, this is a vestigial Ye Olde English use of metric, which should be diminished. Density is the mass of an object divided by its volume. The everyday common volume unit allowed in metric is the liter, and a liter of water is essentially a kilogram. This means that a liter of water has a density which may be written as 1000 grams/liter. Both grams and liters are familiar units in the everyday world of an average person in a metric country. If a wood’s density is below 1000 grams/liter it will float, if it is above 1000 grams/liter it will sink. This is a nice Naughtin’s Laws friendly way to express water’s density, and it does not involve recalling a number like 62.5 pounds per cubic foot. This method essentially relates the specific gravities of the woods in an elegant fashion. It allows one to rationally list the densities of various woods in a way which one can immediately realize if they would float or not:

Wood Density (g/L)

Balsa 96

Yellow Pine 650

Maple 704

Hickory 816

Water Gum Tree 1000 (Density of water)

Black Ironwood 1040

Poison Ash 1104

Arapoca 1200

Lignum Vitea 1229

Qeubracho 1393

Balsa is the lightest of the woods and a cube of it will clearly float in water. Yellow Pine, Maple and Hickory will also all float in water. Yellow pine was chosen for use in the caissons that were used to construct the Brooklyn Bridge.^{[1]} Southern Yellow Pine was chosen for it’s ability to withstand large pressure and for the considerable amount of resin it contains. This makes it very resistant to rotting. Wood from the aptly named Water Gum Tree has neutral buoyancy, that is, it has essentially the same density as water and is compelled to neither float nor sink in it. A block of Water Gum Tree wood is like a helium balloon which floats at a stable position, neither rising nor falling to the floor. The word Quebracho means “Ax Breaker.” Given its high density, this name seems appropriate.

In his last sentence Vergara states: “Since wood weighing more than 62.5 pounds per cubic foot will sink, it can be seen that many kinds of woods cannot possibly float.”

This is true for a single monolithic block of wood, but all these woods can be used to make vessels which will float, they only need to displace enough water to do so. The Civil Engineering students at Iowa State University each year create a concrete canoe. The density of concrete? It’s 2400 grams per liter. But concrete is not nearly as dense as steel which is about 8000 grams per liter. The hollow interior of a canoe or ship decreases the overall density of the ship enough to bring it well below the 1000 grams/liter threshold, which in turn allows it to float. Allowing for shaping, all wood will float.

I very much encourage the use of grams/liter for expressing density. I completely discourage the use of the cgs leftover, grams/cubic centimeter. In the case of steel its density is 8.05 g/cc. I also mostly tend to discourage the use of kilograms per cubic meter, as the units are out of the range of everyday measurement experience. It is, however, very easy to convert from kg/m^{3} to g/L. For instance, the density of steel is 8000 kg/m^{3} which is 8000 g/L. The conversion factor is one. The numerical values are the same, just change the units. It’s just that easy, as the metric system is, and should be, when it’s employed in an articulate manner. People who insist on using Ye Olde English units like pounds per cubic foot—are just dense.

[1] *The Great Bridge*, David McCullough, Simon and Schuster, New York pg. 174-175.

The problem with your grams per liter units for density is that in engineering density is used in many engineering calculations. The metric system is only coherent when the units are expressed as base or derived units without prefixes. For density, the coherent units in calculations are kilograms per cubic meter, that is why it is so commonly used. Fortunately, the conversion is only multiplying by one, but to do it formally, one must remember the definition of the liter as a special name for 1 dm³ and manipulate prefixes, At least it is better than converting between pounds per cubic foot and ounces per cubic inch.

The liter is not an SI unit, although it is accepted for use with the SI, and it is non-coherent in engineering calculations.

More in keeping with your article, did you find any woods with densities in the narrow range between the density of ocean water and fresh water? That might make for an interesting experiment.

Even bigger than Iowa State University’s concrete canoes were the artificial harbours, code-named “Mulberries” used to supply the Allied forces after the D-Day invasion in World War 2.

(http://www.historylearningsite.co.uk/mulberry_harbour.htm)

These were built with 144 000 tons of concrete and 105 000 tons of steel and towed across the Channel using their own buoyancy to stay afloat.

Note: This is a British web site, so the “ton” referred to above is probably the Imperial long ton of 2240 pounds or 1.017 megagrams.

You really can’t be sure. It may have been from a British website but it can also be from an American source. More often then not, the prefixes to the ton, short, long and metric, are often ignored and the various meanings are mixed or confused. People will visualise all of these tons based on their personal feel for the word ton.

The American NIST propagates the problem by insisting the tonne be spelled metric ton.

At least the long ton and the tonne are so close they can be treated as the same. So, 1 long ton would be 1 t or 1 Mg. You can’t know for sure by the website alone if those nice rounded values were exactly that and what the tolerances actually were. Thus trying to use exact conversion factors for approximations ends up with a metric value that is wrong and made to look ugly.

You should know better that 8.05 g/cc is incorrect. It is 8.05 g/cm³.

Also 1 kg/L is the same as 1 t/m³ or 1 Mg/m³

I guess I have to go beyond my original comment and call out as absurd the statement, “What struck me even more was that I was still going along with all the people who use kilograms per meter cubed. In my view, this is a vestigial Ye Olde English use of metric, which should be diminished.”

The fact is that the BIPM, hardly a bastion of Ye Olde English usage, calls out in Table 2 of the SI Brochure that the coherent SI derived units of density are kg/m³. When I have a conflict between choosing you and the BIPM as final arbiter on SI matters, I think I have to go with BIPM (or NIST on Americanizing the spelling, otherwise they conform).

Your recommendation on SI usage should at least fall within the options accepted by BIPM and not directly contradict.

The subject of this essay is objects floating or not floating in water. I noted the absurd 62.5 pounds per cubic foot. What does this value immediately tell one about the density of a material?—not much. Specific gravity is a very common measure using water as a mass base. The density per unit volume in Ye Olde English or metric does not instantly give you any feeling for the density of a material, or whether something will sink or float. That is why I used the word vestigial: because it is like Olde English, if not as ill-formed.

When the liter is used, and people recall that a liter of water is 1000 grams or 1000 g/L it gives one an intuitive benchmark. It is a logical point with which one can teach and express densities. A person recalling 1000 grams are in a liter of water knows that an object of 2000 g/L will sink and an object of 500 g/L will float. Is this automatically true for one of 500 kilograms per cubic meter? This expression of density (g/L) is rather useful, and integrates intuitively with the original definition of the kilogram. In my view non-intuitive pedantry can be a problem and can be a real hindrance to metric acceptance.

You may have noted my trepidation by the fact that I used the word diminished. I understand the usefulness of an expression of kilograms/cubic meter for direct computation. In an upcoming essay I will show this is the case. In the meantime I can tell you which expression I think is more intuitive.

I look for measurement expression which is meaningful, and not slavishly dependent on accepted norms.

And I find the word “diminished” a problem. People should NOT be led away or discouraged from using the proper units of density.

Had you explained that the coherent units of density are kg/m³, but that might be hard to visualize for some and shown how that “converts” with unity multiplier to g/L, I could have accepted that.

You essays are about the title subject with a heavy dose of your views on how to use the metric system correctly. When those views are at odds with the BIPM, I think it is appropriate to speak up. Hopefully, by airing our differences, readers can hear both sides and make up their own minds.

To-may-to, to-mah-to.

This is as absurd as arguing about whether a female celebirty should put her hair in a braid or in a ponytail.

Maybe the Maven hasn’t enough material for three times a month anymore. Maybe once a month, or once in two months, would suffice.

The (new) liter should ideally be one cubic meter, and, at the same time, the kilogram should become one new, redefined gram (or another sensibly named unit), or else we should adopt the tonne as the base unit for mass: this would solve the incoherencies of the current liter being one cubic decimeter (thus, with a now non-recommended prefix), and the kilogram still being a rather strange base unit, with a prefix, while certainly it should have none.

Already said: but SI needs some reforms, anyway…

The volume of 1 cubic metre is or was called a stere. This unit should be put into general use. The prefixes would be in increments of 1000, since we are referring to volume. Thus:

1 decistere would equal one cubic decimetre or the present litre.

1 centistere would be one cubic centimetre.

1 millistere would be one cubic millimetre

1 dekastere would be one cubic dekametre

1 hectostere would be one cubic hectometre

1 kilostere would be 1 cubic kilometre

etc.

The same would be true for area:

The ar should be made to equal one square metre.

The decar should be one square decimetre

The centar should be one square centimetre

The millar should be one square millimetre

The dekar should be one square dekametre

The hectar should be one square hectometre (as it is presently)

The kilar should be one square kilometre.

etc.

SI is missing area and volume units and this would fill in the gaps.

A decistere is 0.1 m or 100 L (a cube 4.641 589 dm on a side). You should review how prefixes work. All of your prefixed steres and ares are wrong.

The stere is an obsolete, pre-SI unit, deprecated decades ago, like the calorie. (Also note 1 kL = 1 st, making it pretty unnecessary).

The BIPM spells the unit of 10 m² as “are” not “ar” although the are is withdrawn and only the hectare is left.

Other than these non-SI special names accepted for use with the SI, area is based on length² and volume on length³, at least according to the BIPM and the SI. USC and Imperial have plenty of obsolete units for you to use.

As far as I know the BIPM nor any other organisation addresses the definition of the prefixes beyond linear applications. In order for area and volume units to be coherent and consistent within SI, when applied to area, the prefixes would become the linear values squared. For volumes they would become the linear values cubed.

Your way is very confusing and incoherent. Your way the cubic DECImetre becomes a millistere, a cubic centimetre becomes a microstere, etc. The farther you go from the base unit, the more the prefixes diverge.

My way, there is coherency. A cubic DECImetre becomes a DECIstere, a cubic CENTImetre becomes a centistere, etc. You can not make it more simple to follow and understand.

In a response to your post on reddit, I explained my reason for suggesting “ar” versus “are”. But in reality it doesn’t matter. I also answered some of your other points.

BIPM says the unit attaches to the prefix, and any exponent attaches to the combination of prefix and unit. 1 dm³ is a cube 1 dm x 1 dm x 1 dm. Of course, it can be other dimensions that multiply to same result. A factor of 10X in all three length dimensions scales a volume by 1000X.

However, if you invent a name for volume it has no exponent (rigorous, it does , but it’s one), a change of ten in prefix would change the volume by ten as prefix attaches to the unit and becomes whole.

See section 3.1 of SI Brochure, last few paragraphs, especially the one containing “new inseparable unit,” and read the part about positive and negative powers. Fully addressed, and it’s not “my” way, it’s the “BIPM’s way.”

Your use of prefixes is absolutely wrong.

kilo means 1000, kilostere 1000 stere. But, for a kilostere to be equal to 1 cubic kilometre, then that would be 1,000,000,000 stere. Similarly, your millistere would not mean 0.001 stere, but instead means 0.000000001 stere (1×10^-9).

1 kilostere is 1000 stere so 10 cubic meter of wood.

Officially nobody use steres in Europe any more!

sorry 1000 cubic meter of wood