A single mix-up of units has erased a $300-million spacecraft, stopped an airliner's engines mid-flight, and left the two halves of a bridge at different heights. This is a museum of accidents that proves, with both laughter and hard lessons, that units really are at the heart of science. Walk through them in order, from oldest to newest.
1492 Funny story
Columbus and the Mile Mix-Up
In 1492, Columbus set sail convinced he could reach Asia by heading west. A famous story holds that, in estimating distances, he confused miles of different lengths and underestimated the size of the Earth, badly underestimating how far Asia really was (historians read the sources in several ways).
What went wrong
The distances given by earlier geographers were written in Arabic miles, but Columbus is said to have read them as shorter Italian (Roman) miles. Combined with an Earth he reckoned too small, this led him to estimate the voyage from Europe to Asia as far shorter than it truly is.
Outcome
He reached land sooner than expected and was convinced it was Asia (the Indies). What he had actually reached were the islands of the Caribbean — a New World unknown to Europe. Ironically, a miscalculation led to a 'discovery' that changed history.
Lesson
Units with the same name can have different lengths across regions and eras — the mile is a classic example. When you quote a number, check which definition of the mile it uses. And as with this tale, because the sources can be read in several ways, it pays to tell such stories carefully, as anecdotes rather than settled fact.
In 1628, the warship Vasa — built to showcase Swedish power — capsized and sank just after leaving Stockholm harbor on her maiden voyage, caught by a gust of wind. The main cause was poor stability from heavy guns mounted too high, though a popular theory also blames the use of different 'feet' during construction.
What went wrong
The chief cause of the capsize was that too many heavy cannons were placed on the upper decks, raising the center of gravity and leaving the ship without enough stability. On top of that, later study of the hull suggests the craftsmen may have used feet of different lengths (a Swedish foot of 12 inches and an Amsterdam foot of 11 inches), leaving the hull slightly asymmetric — but this is offered only as a contributing theory.
Outcome
Vasa had sailed barely 1,300 meters when a first gust heeled her sharply; a second gust let water pour in through the open gun ports, and she sank, with many lives lost. The hull was raised almost intact in 1961 and can be seen today in a dedicated museum in Stockholm.
Lesson
Even with grand figures and fine drawings, the whole goes wrong if the standard for your measurements isn't shared. Yet the heart of this tragedy was choosing show and firepower over safety and stability. When telling history, it matters to separate the appealing 'unit-mistake' theory from the established main cause.
In the 1980s, A&W took on McDonald's 'Quarter Pounder' with a burger that offered more meat — a third of a pound — for the same price. Yet it flopped, because many customers thought 'three is smaller than four' and assumed they were paying the same for less beef.
What went wrong
The problem wasn't a unit but a sense of fractions. Looking only at the denominators 3 and 4, many customers reasoned that 'since 3 is less than 4, one-third must be smaller than one-quarter'. In reality a third of a pound is more, but people felt they were getting less meat for the same money. Note that this was A&W, not McDonald's.
Outcome
Even though the burger offered more beef for the same price, it barely sold. Later market research revealed that many customers had simply mixed up the fractions, and the episode became a famous illustration of how unreliable our intuition for numbers and quantities can be.
Lesson
A correct number is worthless if it doesn't get through. It often helps to say '33% more' or '150 g of beef' instead of 'one-third', matching the way people actually think. Units and fractions only do their job when you design not just the arithmetic but how the message will be understood.
In 1983, just after Canada switched from imperial units to metric, an Air Canada Boeing 767 ran out of fuel in mid-flight because of a unit mix-up in the fuel calculation. With no engines, the captain glided the airliner onto a closed former air-force base at Gimli — and not a single person died.
What went wrong
When working out how much fuel to load, the crew confused pounds (lb) with kilograms (kg). Because a pound is only about 0.454 kg, the aircraft was filled with roughly half the fuel it actually needed. The switch to a brand-new aircraft and to the metric system happened at the same time, and no one's check caught the error.
Outcome
Over Manitoba, first one engine and then the other flamed out from fuel starvation. The captain, an experienced glider pilot, soared the powerless jetliner down to the runway of the closed Gimli air-force base, by then partly used for racing. No one was killed, and the aircraft was later repaired and returned to service.
Lesson
The transition between unit systems is exactly when accidents are most likely. When old and new units mix, the habit that saves lives is to ask independently whether a result is 'about the right size'. And as this story shows, even in the worst case, training and a cool head can change the outcome.
In 1999, NASA's Mars Climate Orbiter failed to enter orbit around Mars and was never heard from again. The cause was a mismatch in the units of force between the ground software and JPL's navigation software — one of the most famous unit mistakes in history.
What went wrong
Ground software built by Lockheed Martin reported thrust in pound-seconds (lbf·s), an imperial unit, while JPL's navigation software took those numbers as newton-seconds (N·s) in SI. No conversion was ever performed between the two, so the force values that shaped the trajectory were off by a factor of about 4.45 the whole way.
Outcome
Flying on faulty navigation data, the orbiter dipped to roughly 57 km above Mars — far lower than the planned altitude — where it is believed to have been destroyed by atmospheric pressure and heat, or to have skipped off and flown past the planet. The spacecraft was lost, and the total mission cost came to about $327 million.
Lesson
The boundaries where systems hand data to each other are where unit accidents breed. Spell out the units in your interface spec, attach a unit to every value you pass along, and keep conversions in one place where they can be tested. A single missed conversion can erase years of work in an instant.
Around 2003, Germany and Switzerland built a bridge across the Rhine from both banks at once — and the deck heights didn't match. The two countries used different seas as their 'zero meters above sea level', and then the correction for that difference was applied with the wrong sign.
What went wrong
Germany referenced the North Sea (the Amsterdam datum) while Switzerland referenced the Mediterranean (the Marseille datum), a difference of about 27 cm. The engineers knew about this gap, but applied the correction in the wrong direction (with the wrong sign). Instead of cancelling out, the difference doubled, and the two banks ended up about 54 cm apart in height.
Outcome
Fortunately, nothing as serious as a collapse occurred; the banks were joined by lowering the deck on the Swiss side. Still, the mistake caused extra rework and cost, and the bridge became a widely told parable of the confusion that a mismatched reference level can cause.
Lesson
It isn't only the number that counts as a unit — so does what that number is measured against. The same 'altitude' means different things depending on the reference surface. Fix one datum, origin and direction (sign) for the whole project, and always double-check that you haven't applied a correction backwards.
Was a spacecraft really lost because of a unit mistake?
Yes. In 1999, NASA's Mars Climate Orbiter was lost because the ground software reported a force in pound-seconds (imperial) while the navigation software read it as newton-seconds (SI). Because the conversion was never made, the trajectory calculations drifted, and the probe entered the Martian atmosphere far lower than planned and was destroyed. The total loss came to roughly $327 million.
Why is mixing metric and imperial units so dangerous?
The same number for a force or a weight means something completely different depending on its unit. Units that look similar — pounds and kilograms, pound-seconds and newton-seconds — are the easiest to confuse, and a forgotten conversion still produces a number that 'looks fine'. When several teams or programs work together, the fix is to fix the unit agreement in writing (the interface spec) and to attach a unit to every value.
Can these unit mistakes still happen today?
They are hard to eliminate completely, but they can be greatly reduced. State the unit on every value, check units automatically when data passes between systems, standardize on SI (the International System of Units), and keep all conversion logic in one tested place. The strongest defense is a culture that treats a unit not as decoration but as part of the number itself.