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# “Watch Your Units!” Part 1 – Even Columbus Had Trouble With Units

Posted October 12, 2018 12:00 AM by RSBenner
Pathfinder Tags: columbus Conversion unit

“Watch your units!” If you polled engineering students, many of them would tell you that this is the phrase most often repeated by professors throughout their college career. And with good reason! It is so easy to calculate an incorrect result to a problem when you fail to notice that some of the starting values are given in different systems of units. Without that initial conversion, there is no hope that your answer will be correct, regardless of how good your engineering is. As students, we often brushed the warning aside as not being a big deal. However, it is a big deal! In fact, I found enough examples where this warning was not heeded, that I wrote multiple articles. In honor of Columbus Day and the landing of Columbus in the Bahamas on October 12, 1492, here is part 1.

“In fourteen hundred ninety-two; Columbus sailed the ocean blue.”

I remember learning this little rhyme when I was in elementary school. We learned all about the explorer Christopher Columbus and his famous travels as he attempted to sail west from Spain to reach Asia and the East Indies. What I did not learn was that part of the problem with Columbus’ voyages (besides the fact that North America was in the way) was that he had a unit conversion problem.

Although not always accepted, it has long been known that the Earth is shaped like a sphere. In fact, the first accurate calculation of the Earth’s circumference was performed way back in the third century BC by the Greek scholar Eratosthenes. An astronomer from Baghdad during the 9th century, Alfraganus, also calculated a slightly less accurate circumference. While preparing for his journeys, Columbus studied the work of both these men, ultimately deciding to use the latter values for use in his own calculations.

According to the work of Alfraganus, one degree (at the equator) is equal to 56.67 miles. In addition to using this less accurate number in his calculations, Columbus made another error. He wrongly assumed that Alfraganus was using the 4,856-feet Roman mile when he actually meant the 7,091-feet Arabic mile. This resulted in a 25% reduction in Columbus’ calculated circumference size. In addition, Columbus thought Japan was located at 85 degrees west longitude rather than 140 degrees east. These miscalculations resulted in a 58% margin of error in his estimate of the distance it would take to reach the East Indies.

Throughout Columbus’ life, he never accepted that he did not reach Asia during his voyages. Perhaps if he had used the findings of Eratosthenes, and performed the correct unit conversion, he would have realized he had actually reached the “New World.”

Stay tuned for Part 2!

Reference:

https://spectrum.ieee.org/tech-talk/at-work/test-and-measurement/columbuss-geographical-miscalculations

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#1

### Re: “Watch Your Units!” Part 1 – Even Columbus Had Trouble With Units

10/12/2018 9:38 AM

A bigger problem for Columbus was "the Longitude problem". Using celestial navigation to find longitude requires knowing what time it is. An accurate clock that could be taken aboard ship was not developed for another 200 years after his voyage. The alternative, dead reckoning, is not very accurate on the ocean, given the lack of landmarks.

http://theconversation.com/the-longitude-problem-how-we-figured-out-where-we-are-16151

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#2

### Re: “Watch Your Units!” Part 1 – Even Columbus Had Trouble With Units

10/12/2018 3:26 PM
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#3

### Re: “Watch Your Units!” Part 1 – Even Columbus Had Trouble With Units

10/12/2018 7:15 PM

Not quite as historical, but "Watch your Units" was always heard from every slide-rule toting professor that I had in USN and college!

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#12

### Re: “Watch Your Units!” Part 1 – Even Columbus Had Trouble With Units

10/18/2018 3:51 PM

Would that be a wide yellow slide rule?

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#4

### Re: “Watch Your Units!” Part 1 – Even Columbus Had Trouble With Units

10/13/2018 10:01 AM

If I recall correctly, the crash of a space craft on Mars was found to be a units error--one group calculated in Metric units and another was using English units.

--JMM

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#6

### Re: “Watch Your Units!” Part 1 – Even Columbus Had Trouble With Units

10/13/2018 4:13 PM

Ashes to ashes, dust to dust....

..."September 23, 1999, communication with the spacecraft was lost as the spacecraft went into orbital insertion, due to ground-based computer software which produced output in non-SI units of pound-force seconds (lbf·s) instead of the SI units of newton-seconds (N·s) specified in the contract between NASA and Lockheed. The spacecraft encountered Mars on a trajectory that brought it too close to the planet, causing it to pass through the upper atmosphere and disintegrate.[1][2] "...

..."The discrepancy between calculated and measured position, resulting in the discrepancy between desired and actual orbit insertion altitude, had been noticed earlier by at least two navigators, whose concerns were dismissed because they "did not follow the rules about filling out [the] form to document their concerns". A meeting of trajectory software engineers, trajectory software operators (navigators), propulsion engineers and managers, was convened to consider the possibility of executing Trajectory Correction Maneuver-5, which was in the schedule. Attendees of the meeting recall an agreement to conduct TCM-5, but it was ultimately not done.[17] "...

..."NASA assigned three separate teams to investigate the embarrassing, US \$125 million debacle and determine its cause. Preliminary public statements faulted a slip-up between the probe's builders and its operators, a failure to convert the English units of measurement used in construction into the metric units used for operation.

After six weeks, on 10 November, NASA officials released their preliminary findings. However, an IEEE Spectrum investigation had been going on separately, using unofficial sources associated with the program and independent experts. Spectrum quickly learned that far more had gone wrong than just a units conversion error. A critical flaw was a program management grown too confident and too careless, even to the point of missing opportunities to avoid the disaster.

As reconstructed by Spectrum, ground controllers ignored a string of indications that something was seriously wrong with the craft's trajectory, over a period of weeks if not months. But managers demanded that worriers and doubters "prove something was wrong," even though classic and fundamental principles of mission safety should have demanded that they themselves, in the presence of significant doubts, properly "prove all is right" with the flight. As a result, the probe was about 100 kilometers off course at the end of its 500-million-kilometer voyage--more than enough to accidentally hit the planet's atmosphere and be destroyed."...

https://spectrum.ieee.org/aerospace/robotic-exploration/why-the-mars-probe-went-off-course

https://en.wikipedia.org/wiki/Mars_Climate_Orbiter

N to lbf = N X 4.448222

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#10

### Re: “Watch Your Units!” Part 1 – Even Columbus Had Trouble With Units

10/15/2018 7:59 AM

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#9

### Re: “Watch Your Units!” Part 1 – Even Columbus Had Trouble With Units

10/15/2018 7:58 AM

That was one of the causes of that crash, yes. I talk about that in part 2 of this series!

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#5

### Re: “Watch Your Units!” Part 1 – Even Columbus Had Trouble With Units

10/13/2018 11:08 AM
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#7

### Re: “Watch Your Units!” Part 1 – Even Columbus Had Trouble With Units

10/14/2018 12:16 AM

The fact is that Christoper Columbus was the last to discover the new world America We have all been brought to lye's and miss information in our schooling ! I wonder what Our New Children are Taught ?

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#8

### Re: “Watch Your Units!” Part 1 – Even Columbus Had Trouble With Units

10/14/2018 2:28 PM

Columbus was the original entrepreneur...

It turned out he set off on a journey to an unknown place, without knowing how to get there, without knowing where he was when he got there, and without knowing where he had been when he got back..

............and he did it all with the King of Spain's money.

Incredibly brave to my mind, and an amazing story in self-belief and commitment.

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#11

### Re: “Watch Your Units!” Part 1 – Even Columbus Had Trouble With Units

10/15/2018 10:14 AM

Or a good story in how to manipulate people into paying for your trip before you even had it planned. How to justify the means for the end? How to take what should be other peoples' fame? How to shoot blindly in the dark? How to think you know what your doing and, even when you are wrong, be dead-set that you are right? Columbus is a sham. You can try to teach luck, but statistics will set the curve.

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