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“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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