Systems of units

I am sure that somewhere there is a definitive history of systems of units. We are still in a dreadful muddle with units and the muddle shows no sign of disappearing. We need to see why.

 

First we must decide what we mean by units. Perhaps we should start by looking at weights and measures. Probably there was not any problem with weights and measures at one time. They were needed for commerce. Initially when the number of sheep that could be traded for a given herd of goats only a system of numbers was needed and that might only be a tally stick. But once a commodity like grain or salt is to be traded for money a system of packing commodities in known quantities was needed. All sorts of “standard” quantities were used and often these quantities were peculiar to the trade involved. There was nothing wrong with this although one can imagine that there were opportunities for sharp practice in every transaction[1]

 

There was a common feature to these measures. They were chosen to suit the commodity. Grain was sold by the sack-full but diamonds weren’t. The proliferation of weights and measures no doubt led to sharp practice and some limit could be placed on this if some legal system of weights and of length could be established.[2] Arbitrary systems were established in various countries and colonialism ensured that some were promulgated across the world. It was inevitable that commerce would have to proceed with this mixed bag of weights and measures. To the practitioners of trade this was probably no problem and, if busybodies in politics and science had kept out of it there would be no problem.

 

Then came the rise of science. Now there were people who had to think about units for a different reason to those engaged in commerce. In the 17th century Newton pointed out that mass and weight are not the same thing and the problems started. Scientist wanted not a system of weights and measures but a system of units. They observed that, if you started from the unit of length, now measured to some staggering accuracy, all the measures of volume could be expressed in cubic feet or whatever the unit was. But cooks knew in their bones that a pinch of salt could never be measured in cubic feet and retain any meaning.

 

Scientists went one better. They could see that you could have a system that allowed every physical quantity that could be imagined to be related to each other by one set of specified units for length, mass, time and temperature and a few others. They called this a consistent system of units. The still went shopping in the ordinary measures of course but some, who liked to be in control, could not but feel that it would be nice if everybody was forced to used a consistent system of units regardless of the snags.

 

The snags were mainly that these new consistent units are often extraordinarily small compared with the size of thing to be measured or, of course, extraordinarily large. We have enough trouble with imagining size because people live most of the time in a people-sized world. We do not often sit and contemplate the flow over the Niagara Falls or the size of a molecule of gas nor yet the fact that spiders have working knee points. Should we do so we find that ordinary units do not convey any idea of the magnitudes involved. What we do not want is to find that the ordinary units do not convey an idea of magnitude when they are used for ordinary things. The metric system was based on an arbitrary length derived from the circumference of the Earth. Users of the system devised all sorts of non-preferred units to make the units fit the size of the thing to be measured which is of course our starting point. I suppose they were comfortable with them. I lived in a world of feet and inches and pounds and ounces. Doing physics and electrical calculations in grams and centimetres caused no great problem to those trained in science, one simply got used to two systems. All these units were people sized.

 

However calculations for electrical engineering gave rise to ordinary quantities measured in millions or millionths and they fancied the metre, kilogram, second system because it fitted their calculations better. Then, when Britain joined the European Union, the question of units got tangled up with the decimal system versus the duodecimal systems. Everyone forgot how easy it is to work in two systems and persuaded Britain to move to the SI system of units that was a derivative of the MKS system. Suddenly lorries appeared with their weights painted on the back in kilograms instead of tons or tonnes and in Newtons. No doubt the French lorry drivers were just as mystified by weights in Newtons as everyone else. It was a great triumph for the scientific lobby over good sense. No one puts weights in Newtons now because the process of common sense is at work devising new non-preferred units to make the numbers intelligible to ordinary people.

 

Unfortunately the SI system does not fit with mechanical engineering and we are lumbered with it. If you want to buy petrol you are charged by the litre but you cannot buy a single litre of petrol. The next preferred unit is the cubic metre! When I asked a group of engineering students from overseas who had all been brought up using the metric system to say how many cubic metres of space there is in a mini car they simply had no idea. They had never thought in cubic metres before.

 

Our current position is that an engineer trained in the SI system will go to work in organisations using all sorts of hybrid systems of units. They will meet new designs with metric and Imperial dimensions in the same component because the firm is taking advantage of cost and availability. Standardisation is a far off dream and we have to work in one system now and expect to adapt to circumstances as they arise. One unforeseen consequence is that if a customer is paying for design calculations and these calculations are in some incomprehensible units like Newtons per square metre he cannot check to see whether they make sense in the ordinary concept of common sense. It is a paradise for rogues.

 

So what systems of units have been used? The most commonly used systems are the Imperial system and the Metric system.

 

In the Imperial system one pound force (denoted lbf) will give a mass of one pound an acceleration of 32.2 feet/second. In the system in common use in Europe 1 kilogram force (denoted kgf or kilopond) will give a mass of 1 kilogram an acceleration of 9.81 metres/second

 

Other systems have been used. The ones I know about are:-

the dyne-gram-centimetre-second system (C.G.S.) which was certainly in use in school physics. The gram is a very small mass to be a unit and the dyne a very tiny force. But it was used for small scale applications and seemed to be workable for these.

the poundal-pound-foot-second system which had its adherents but was not very popular because the poundal, being equal to 1/32.2 lb was too small a force to be an acceptable unit.

the pound force-slug-foot-second system much used in aeronautics. The slug has a mass equal to 32 2 pounds but the name for the unit of mass was somehow repulsive and it was really too large.

 

Before the arrival of the SI system most people worked in either the Imperial system or the metric system. They accepted the pound force and the pound mass or the kilogram force and the kilogram mass and used the appropriate value of g to make calculations. Then forces and masses were measured in people-sized units.

 

In Great Britain the driving force behind the change to the SI system was the National Physical Laboratory. They published the rationale for it in a pamphlet called “Changing to the metric system”(published in June 1965), a title which was misleading (probably deliberately) because the change was to the new SI system. That rationale looks to be just as dubious now as it was then and the introduction of a consistent system of units with all its problems was hidden under the argument that working in tens is better than working in a mixed collection of factors even if these factors were more suitable for the task in hand. One is forced to wonder what system of units the NPL used when they claim that the Imperial system was the yard-pound-second system. I have never seen g quoted in yards/sec/sec.

 

The Systeme Internationale d'Unites (S.I.) is the Newton-kilogram-metre-second system. This is really a metric version of the old poundal-pound-foot-second system with the same old problems. The unit of force is small. However journalists, politicians and academics joined forces to give the SI system the backing of the law and we are stuck with it. I suppose that the consequences of the introduction of the SI system can be typified by one example. A cubic centimetre that could be imagined by anyone was suddenly the millilitre a descriptive word that simply defies the imagination. Units derived by some arcane formula and a hierarchy simply create confusion for the vast majority of ordinary people who are not technically trained. The man digging a hole in the road claims that it is one and a half metres deep and he knows this because he has been told that his shovel is a bit less than a metre long. What is his unit of length, the metre or the shovel? I say to students of engineering that your task has been made more difficult by the SI system and it is essential for you to understand it and be able to understand other systems so that you can switch around as the need arises. If you set about it with a will it is really quite easy.

 

The S.I. unit of force is the Newton, a large hen's egg weighs about 50 grams and that is about a half a Newton, and, as the consistent unit of area is the square metre, the unit of pressure is 1 Newton/square metre. The diagrams for this book were drawn on good quality note-paper weighing 100grams/square metre so a single sheet of that paper would exert a pressure of nearly Newton/square metre (one Pascal) on any horizontal surface on which it was placed. It is clearly not a tangible pressure. An insect can crawl from under a sheet of paper. In these units the atmospheric pressure is about 100,000 N/square metre. Power engineers did not fancy swapping pounds/square inch or kilogram force per square centimetre for Newtons/square metre and the galactic numbers that would be entailed so they put 100,000 Newtons/square metre equal to 1 bar and got on with their work. What is the man who wants to pump up the tyres of his car to do when he finds the tyre pressure quoted in Pascals, bar, and pounds/square inch?

 

Nor is it easy to comprehend the magnitude of the unit of pressure. Clearly the S.I. system is not ideal, it may fit science but it does not fit people.

 

The fact is that the S.I. system was introduced at a time when two other systems, the foot-pound-second system and the metric system (the kgf-cm-second system), were well established. They are systems which make sense to ordinary people when used to measure ordinary things and are used quite easily in science and engineering. It is 40 years since S.I. was introduced yet it is still not in general use. In practice many non-consistent secondary units are still used and others evolved to suit particular applications. Governments may legislate to enforce the use of some preferred system but, in time, as its deficiencies become evident and the offending politicians find different things to worry about, the will to enforce the system wanes and modifications are introduced or, the former systems are revived.