There Is No Such Thing As An Invalid Unit


The Mars Climate Orbiter was a spacecraft launched in the closing years of the 1990s, whose job was to have been to study the Martian atmosphere and serve as a communications relay point for a series of other surface missions. It is famous not for its mission achieving these goals, but for the manner of its premature destruction as its orbital insertion brought it too close to the planet’s atmosphere and destroyed it.

The ill-fated Mars Climate Orbiter craft. NASA [Public domain].
The ill-fated Mars Climate Orbiter craft. NASA [Public domain].

The cause of the spacecraft entering the atmosphere rather than orbiting the planet was found in a subsequent investigation to be a very simple one. Simplifying matters to an extent, a private contractor supplied a subsystem which delivered a reading whose units were in the imperial system, to another subsystem expecting units in the SI, or metric system. The resulting huge discrepancy caused the craft to steer towards the surface of the planet rather than the intended orbit, and caused the mission to come to a premature end. Billions of dollars lost, substantially red faces among the engineers responsible.

This unit cock-up gave metric-using engineers the world over a brief chance to feel smug, as well as if they were being honest a chance to reflect on their good fortune at it not having happened on their watch. We will all at some time or another have made an error with respect to our unit calculations, even though in most cases it’s more likely to have involved a simple loss of a factor of ten, and not with respect to a billion dollar piece of space hardware.

But it also touches on one of those fundamental divides in the world between the metric and imperial systems. It’s a divide that brings together threads of age politics, geography, nationalism, and personal choice, and though it may be somewhere angels fear to tread (we’ve seen it get quite heated before to the tune of 885+ comments), it provides a fascinating subject for anyone with an interest in engineering culture.

The King’s Foot, And A Cube Of Water

Before we look at those threads and descend into the realm of opinion, it’s worth examining the basis of fact upon which they sit. There are three fundamentals to consider, the origins of the imperial units, those of their metric counterparts, and that when it comes to metrology there is no such thing as an invalid unit, providing that the unit in question has a consistent and valid definition.

Imperial units, at least as far as they are understood where this is being written, are the standardised version of the English system of units as defined by the British government in the 1824 Weights and Measures Act. Prior to that date they had been part of a system of customary mediaeval measurements with roots in Roman and northern European customs including it is reputed, the length of the King’s foot. But of course the astute amongst you will point out that these British units bear some differences from the similar American units. For example, 1 imperial gallon is equivalent to about 1.2 US gallons, which in turn in the metric system is about 4.54 litres. This divergence is accounted for by the two countries adopting different standardisations of the customary units in the decades following American independence.

The metric units with which we are familiar have their legal origins in post-revolutionary France, as a solution to the chaos of customary units that had been a despised feature of French commerce. They were the fruition of proposals that had come from a variety of scientists and thinkers across the European continent throughout the period of the Enlightenment, as for the first time they brought together the definition of a system of measurements not only under a consistent numerical base, but with coherent links between units. Thus a metre was a ten-millionth of the length of the meridian from the North Pole through Paris to the Equator, a volume of 1 litre could be expressed as a cube of side 0.1 metre, and a mass of 1 kilogramme was defined as that of a litre of water. From this beginning has evolved the coherent system of SI (Système international) units, in which all units can be defined in terms of a small set of base units with the same consistent numerical base. The base units may now be largely defined in terms of constants rather than the physical standards of post-revolutionary France, but the elegance and consistency of the system remains.

Reading the thumbnail descriptions of the two systems, I’m sure you will have made up your own minds which you would prefer to use. Very few of you will be sitting on the fence, and you’ll all be prepared to fight your own corners in the comments. But before going there it’s worth making what is probably the most important point on this page, that there is no such thing as an invalid unit. We may prefer to use one or the other for some extremely valid reasons, but there is no reason whatsoever why engineering achievement should be held back by our choice. Consider all the engineering achievements of the past few hundred years that were made by engineers wielding micrometer screw gauges calibrated in thousandths of an inch rather than in milimetres, did they somehow perform less well for their choice of units? The Apollo astronauts might comment that they didn’t.

Doing Time For A Pound Of Bananas

In the United Kingdom, the metric system forms the official as well as the generally accepted set of units. There are however customary exceptions to this, such as pints of milk or beer and distances measured in miles, and it is fair to say that at times it has entered the realm of politics. Metrication came within the same decade as our entry into what would become the European Union, so it was something that could easily be portrayed by politicians with a particular axe to grind as a confusing foreign system imposed from Europe. We’ve had various controversies such as the “metric martyrs”, market traders prosecuted for selling produce by the pound rather than by the kilo, and it’s an issue over which passions can still run high.

As a Brit born a year or two before European Community membership then, it’s a subject of which you might say I have had a grandstand view. As an engineer I use metric units throughout as the obvious choice, yet with formative years in a largely pre-metric era there are still customary Imperial units  with which I am familiar. My car for instance has 35PSI in its tyres and does 70 miles to the gallon on a good run even though I haven’t been able to buy fuel by the gallon for nearly a quarter century, and when it comes to textiles I use inches probably because my mother did.

So if I had to choose a side of the fence upon which to sit on the question of units I guess I’ve made myself pretty clear as a metric user. One of the most enlightening series of lessons of my whole school career was that in which the SI system was explained and in which everything in the world that could be measured fell into order. Once you have had that explained to you it’s difficult to go backwards. But I understand those contractors who inadvertently sent their craft spinning into the Martian atmosphere, and realise that in another decade, it might have been me sitting in their hot seat.

You’ll all have strongly held views on the subject of units, which you’ll no doubt be anxious to share in the comments. But as I mentioned earlier, we’ve already had that discussion.

Given the story of the Mars Climate Orbiter with which we started, it would be most interesting to hear from engineers who have crossed the gap between the different sets of units. The Hackaday readership contains an astonishing breadth of experience. Please share your stories of where a project was saved at the last minute (or perhaps failed in some spectacular way) because of a mismatch in the measurement language used by different parts of the project.



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