Neutrium 1: Unit Conversions

Since the dawn of thinking, mankind has been measuring things. If humans are going to tell each other about all the great counting and measuring they've been doing, they need to put it in terms others can understand. Imagine it's 5000 BC and you are Gorak, the local counting and measuring expert. Your tribe wishes to trade produce with a neighboring tribe. Being the crafty measuring expert you are, you've developed a system for comparing two goods on a mass basis, and thus your unit, Standard Rock, is born. These necessities are the birth of all units, and that is our topic today. - Welcome to the Nutrien Podcast. I'm Trevor Walker. - And I'm Matthew Kidd. - And today we're gonna discuss one of the most fundamental yet often incorrectly performed engineering calculations, the humble unit conversion. - So unit conversions, Trev. I think I remember the first lecture I ever attended at university and I think that was pretty much the topic and I think I've been getting unit conversions wrong ever since. - Nearly every shoot I got poor marks on in first year was due to a unit conversion. - So let's get started. Now to understand the mess that is unit conversions, you need to have a general understanding of the origins of measurement and how it has evolved over time. It turns out the concept of units is quite old, dating back as early as the 3rd millennia BC. Once people came to the realisation that it was a good idea to talk about measurements such as length in terms of a quantity they can easily communicate to each other, they needed to develop units. As you'd expect, the first units were based on the body. It's only natural to describe a length in terms of how many hands or feet long it is. This line of thinking led to units such as the cubit, an ancient Egyptian unit representing the distance from your elbow to the tip of your middle finger. Although the definitions of these units have changed over time, with the foot for example changing from around 296mm in Roman times to its current 304.8mm when it was standardised in 1959. This highlights the primary drawback of using body based measurement, standardisation. Not everyone has the same length hands and feet, so the quantity the unit represents could vary significantly based on who is in power and the geographic location. So when you run out of body parts, and to be honest they're only good for measuring length anyway, you can turn to things around you for inspiration. This often came at a time of technological change to compare new things against the old. Take the horsepower for example, a unit still in widespread use today. It arose at the beginning of the industrial age, as machines began to replace animals. Thus a measure of how many horses a machine could replace would be a useful measure. As electricity began to take root in cities, electric lights came into widespread use. Candle power, as a measure of the intensity of light, was a useful measure of the lighting effects for your fancy new lightbulb. So we picked our examples of units based on the familiar from these dawn of the industrial age examples, but during recent times we've seen a bit of a resurgence thanks to the modern documentary. They've been unsatisfied with the units commonly used in science and engineering and they've constructed their own sets of units. We've got the football field, the Empire State Building, the Olympic swimming pool, the Nimitz class aircraft carrier. Yeah, these units can really be used for any measurement you want such as length, area, mass, volume or some combination of them both. Quite frankly, I think it's a bit of a crime against science and an almost useless system of management used in every documentary about a large object that's been made since 1995. Yeah, an example of what you might hear is, "Saudi Arabia produces enough crude oil in one day to cover 10,000 football fields to a depth of one foot, which is equivalent to filling 600 Empire State Buildings." Personally, these comparisons don't give me much of an insight into the size of anything, and as you might have noticed, they're a bit of a gripe of mine. Documentaries aside, once humanity could describe things in terms of the familiar, the next problem to tackle was standardisation, the overarching theme of unit conversions. The first sense of unit standardisation came through the expansion of empires and trade. Like our friend Gorak, the Romans had to make sure everyone was comparing apples to apples as they traded across their vast empire. This standardisation movement resulted in some of the units we know and hate today, such as the pound and the tonne. The problem was that although standardisation was occurring, many different parties were standardising around their own measures, a practice users of the imperial system have fully embraced. Take for example the mass unit tonne, which originally derived from the wine barrel size called the tonne, spelt T-U-N, and now exists in either the long or short tonne, spelt T-O-N, and the metric tonne, spelt T-O-N-N-E. Needless to say it can be very confusing if people don't specify the specific tonne they are using. And this is not a problem limited to the tonne, it is also a problem with units such as the gallon, pound, ounce and pretty much any unit Americans like to use. of units is not always enough as there are a few different sets of standardised units out there in the wild, and if you mix them up it can all go horribly wrong as NASA found out in 1999. Now the kind of person who would download an engineering-themed podcast about unit conversion might already be familiar with the Mars Climate Orbiter, but for those who aren't, here's the short version. In December 1998, NASA launched a mission to Mars to study the climate and surface and do all those good things that space probes do. The mission cost $328 million US dollars, and the probe weighed 338 kilograms, or 745 pounds, assuming I got the unit conversion right. In September 1999, the craft had finally made its way close to Mars, and began to make the preparations to fulfill its destiny, orbit. This required a series of propulsion bursts to bring the craft to the correct speed and angle. But something wasn't right, the corrections weren't achieving the result that was expected back in mission control. The craft never achieved its destiny, and instead of being the Mars climate orbiter, it became the Mars surfaced impactor, after breaking up in the atmosphere. Perhaps the only useful piece of information the study was able to gather was that Mars has sufficient atmosphere to destroy a climate orbiter that gets too close too fast. The investigation revealed a humble unit error had caused the whole debacle. At the interface between one system and another, there was an expectation for an input in newton seconds, and instead the output was in pound force seconds. A simple unit error had undone millions of dollars and years of hard work. NASA came unstuck because two contractors were using different units to quantify momentum. To help organize units a little better than the haphazard de facto standards spread by trade and empire, efforts were made to develop coherent systems of units. These days there are many systems of units, including the Imperial and US Customary, Metric, CGS which stands for centimetre gram second and FPS which stands for foot pound second. There are many other systems which can differ in the choice of either base or derived units and are often specific to regions or industries. The major global effort to standardise units is the metric system. The French revolutionised the systems of units in 1791, amongst other things, perhaps to help with quantifying the number of heads they had collected. The original metric system set the standard units for mass, length, area and wet and dry volume. This system was slowly spread to different countries. In 1875 the metric system began to be formalised by international treaty and the system was expanded to cover 7 base units we know and love today. The base units for the metric system are the metre for length, kilogram for mass, second for time, ampere for current, kelvin for temperature, mole for quantity of atoms and candela for luminosity. We came so close to having an organised and coherent set of units with the metric system But perfection it seems is not achievable and the system was left with a fatal flaw, the kilogram. None of the other base units in the metric system have a prefix. They're all 10 to the power of zero of their kind. Meter, ampere, second, kelvin, mole, candela, no prefixes there. Apparently the kilogram was originally called the grave, made up of a thousand grams. But degrave or grave got caught up in the French Revolution for being too aristocratic and so it became the kilogram. Along the path of standardization, the metric system became known as either the SI system, the International System of Units, or le système international de units. Probably didn't say that snooty enough. For the ISO nerds out there, ISO 80000-1, International System of Quantities, is where to look for the final word on SI units. I guess the takeaway is, if you want to be a civilized engineer, you should be using the SI system. So let's take a look at some of the technicalities and quirks of units. Starting with base units and derived units. Base units form the building blocks of the SI system. They are the units from which all other units can be derived. As we mentioned previously, the base units are the metre, the kilogram, second, ampere, kelvin, mole and candela. Derived units are everything else and can be formed by multiplying and dividing some combination of the base units. For example, pressure. The pascal is kilograms per meter per second squared. Volts is kilogram meters squared per second cubed per amp. Radians is a bit of a weird one, it ends up with no unit at all, as it's meters per meter. The same process of deriving units is also in the traditional systems, for example psi, which is pounds of force per square inch, of which pound force is also a derived unit, named the same as a unit of mass, just to keep you on your toes. Moving on from derived units, the next quirk we have is temperature. The systems we use to measure temperature are a bit unusual, thanks to their history and the difficulty in finding out what "no temperature" might actually mean. People often get confused about temperature, the property, and degrees of temperature, the unit. There is an important distinction where temperature is a state and degrees is a set change in temperature against a given scale. Temperature is unique in that for most units, zero means the absence of quantity, but in In both our traditional temperature scales, zero is inserted somewhere in the middle, with degrees Celsius being set at about 273.15 Kelvin and zero Fahrenheit being at 459.67 Rankine. To help us understand this madness, we need to explore the derivation of each of the scales. Fahrenheit, like all empirical units, may seem crazy to use as a metric system on the surface, but there is method to the madness. of temperature is quite a difficult quantity to measure without any units, so the Fahrenheit scale was originally specified by what could be practically and repeatedly achieved in the lab. To develop the Fahrenheit scale, they choose two points at which temperature could be reliably reproduced. The first point, at zero on the scale, was set to the equilibrium temperature of equal parts mixture of water, ice and ammonium chloride, which happens to be a frigerific mixture that will reach a constant equilibrium temperature independent of the temperature of its components. The second point at 32 Fahrenheit was chosen as the temperature of equal parts mixture of water and ice, which also happens to be the melting point of ice. Celsius, on the other hand, originally defined zero as the freezing point of water and 100 as the boiling point of water at one standard atmosphere, but since 1954 has been defined by absolute zero and the triple point of Vienna standard mean ocean water. Moving away from the traditional temperature scales we have our new fandangled absolute temperature scales, the Rankine and Kelvin. Rankine has the same differential units as Fahrenheit but zero is set as absolute zero and Kelvin has the same differential units as Celsius but also has zero set as absolute zero. That Vienna standard mean ocean water sounds like the worst marketed mineral water in the world. I don't know why they just didn't stick with the old standard mean ocean water. You can attract a price premium when people think it's from Vienna. So I've got a couple of bones to pick with the temperature scale. Firstly, there's no such thing as degrees Kelvin. It's just Kelvin. But people probably forgive you if you say there is. And Fahrenheit. Coming from a metric country, it seems like the crazy scale, but it has one strength against Celsius, and that is when you're describing the weather. When you're talking in Fahrenheit and you're saying 50, 60, 70 degrees, or temperature in the 60s, 70s, that sort of thing, it actually means something. sort of gives a window where you can you can understand what that will feel like. In Celsius, you say temperatures in the 20s, that ranges from sort of comfortable to really quite hot and temperatures in the 30s ranges from starting to get uncomfortable to man we really need to get out of this heat. I don't know I kind of like the purity of the Celsius scale. You know zero I'll be frozen, hundred I'll definitely be dead and evaporated. Pressure Pressure is another scale that doesn't always start at zero. Absolute pressure is measured as the pressure above an absolute vacuum, but in practice making and maintaining total vacuum conditions is hard. When we measure pressure in the outside world we always have the pressure of the atmosphere pushing back, and this pressure keeps changing like the weather, or more precisely because of the weather. Gauge pressure is the pressure you are measuring above the current atmospheric pressure. As you might guess from the name, almost all pressure gauges you come across will give you gauge pressure. So if you come across a gauge with the units kPa or psi written on it, it's safe to assume you're reading gauge pressure. So if you're looking for the absolute pressure, and you've got a reading in gauge pressure, you need to take that reading and add atmospheric pressure to it. Usually people just take a typical value for atmospheric pressure and don't bother to find out what the actual atmospheric pressure was on the day. So temperature and pressure have difficulties with their scales, but they also cause challenges for measuring liquid and gas flows, and because of this we come up with adjusted units to try and standardize. For liquids, the temperature will affect the density, and for gases, temperature and pressure will affect the density. This is a problem because it's usually very convenient to measure these in volumetric flow rates. So looking at gas, if you have two gas volumes at different temperatures and pressures, how do you compare them? For those of you who said convert the gas to a mass basis, you're correct. But in industries that deal with gas, they like to do it the hard way. We pick a standard temperature and pressure and figure out what the volume of our gas would be at those conditions, so we end up with units like the standard cubic feet, standard metres cubed and normal metres cubed. So you've got to convert your volume or volumetric flow rate from the flowing conditions to a set of standard conditions, which are slightly different depending who you talk to. For standard metres cubed it's 101.325 kPa at 15 degrees Celsius. For normal meters cubed it's 101.325 kPa at 0 degrees Celsius. And for standard cubic feet 14.696 psi and 60 degrees Fahrenheit. So Trev, in practice when you're doing the kind of sloppy engineering like I am, I would tend to almost ignore the difference between 0 degrees Celsius, 15 degrees Celsius and 60 degrees Fahrenheit. Particularly the Celsius and Fahrenheit. It's the difference between 15 degrees Celsius and 15.6 degrees Celsius and that's not going to make a difference to what I'm doing. Yeah you often see people just neglecting the difference or not even aware of the difference but if you're writing large-scale commercial gas trading contracts you might be interested in on the points on the dollar and the other place you really want to get it right is when you're sizing up a relief valve which nearly always is specified in terms of standard cubic meters. Closely related to the adjusted unit we have industry specific units. Industry loves tradition and won't change just because there is a better way to do things now. Industry has managed to hang on to quite a few of their traditional units. For example in the petroleum industry we have the barrel of oil. Many things such as the refineries throughput is quoted in this and oil is still traded in the barrel. But you have to be careful when you're converting between barrels and other volumetric measures because there are many different types of barrel units such as US Fluid, US Dry, Imperial and the barrel of oil equivalent which doesn't even measure volume but instead measures energy. And in addition to these you also have other crazy units such as bushels, MMSCFD which stands for million standard cubic feet per day and terajoules which is used to actually measure a mass flow of gas. Trevor let's not forget about pork bellies. Yeah pork bellies were literally the cut of meat and it was traded on the futures exchange till it fell out of favour in around 2011. A sad loss to the news finance reports when they weren't saying pork bellies every night. This brings us to our final unit category, currency. Currency is in a unique unit in that is not tied to the physical world, at least not since we've moved away from the gold standard. There is no fixed conversion rates between currency and with a floating exchange rate the rate is determined by foreign exchange market trading. So we'll finish the show today with another story of unit conversions gone wrong, the ghimley glider. This one has a bit of a happier ending than our Mars surface impactor though. So on the 23rd of July 1983 Air Canada flight 143 of Boeing 767 took to the air departing Montreal and heading to Edmonton. This should have been a typical uneventful domestic flight but on this day the Swiss cheese of safety nightmares lined up. There'd been trouble on the ground before the flight with the maintenance staff struggling to deal with both fuel gauges been broken. Eventually, for some reason, it was decided that if they knew how much fuel had been loaded and the fuel burn rate, it was ok for the plane to take off with no working fuel gauges. The flight crew and ground crew set about calculating the required amount of fuel, each using an incorrect conversion factor. Canada was in the process of converting to the metric system and people weren't completely comfortable with it yet, so the factor for pound was used instead of kilograms. Because of this, the aircraft ran out of fuel at cruising height about halfway through its flight. This is the kind of result you might expect if you only load about half the required amount of fuel onto your plane before a flight. But fortunately the captain was an experienced glider pilot and the first officer was a former Air Force pilot who knew about a now closed airbase in the area. Ultimately the plane was forced to perform an emergency gliding landing at the former Air Force base at Gimli and it was then a motorsport complex. There were some injuries but no fatalities. Ultimately there were two root causes of the incident. A failure of management of change and procedures which led to the plane being allowed to take off without any working fuel gauges. This partly stemmed from the fact that the 767 was a new aircraft but really it was just a failure of procedure. And then there was the failure of the unit conversion. At the time when they were changing over from Imperial to metric units they used pounds instead of kilograms and with one being roughly half the other they only ended up with half the fuel on board. As a result of this incident the pilots were punished for getting themselves into the mess. The captain was busted down to first officer and the first officer was suspended. Later they put several pilots through a flight simulator to see if they could replicate the landing but none of them could. In 1985 the pilots were awarded the first ever Federation Aeronautique Internationale diploma for outstanding airmanship. Even though the plane landed without a nose gear deployed it was able to be returned to service and finally retired in 2008. A lucky escape from what would have been almost certainly the worst unit conversion related disaster in history but maybe because they got away with it the Mars impactor takes the crown. Hopefully we've given you some background and insights that will make you less prone to errors or at least more aware of the places you can make the errors. Okay and that brings us to a close. Thanks for listening to the first episode of the Nutrium podcast part of the Engineered Network. For further information on unit conversions check out the show notes and if you want some light reading check out www.nutrium.net