Part One from Engineering 360
“Watch Your Units!” Part 1 – Even Columbus Had Trouble With Units
“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!
“Watch Your Units!” Part 2 – The Space Program
“Watch Your Units!” Part 2 – The Space Program
“Watch your units!” There is that phrase again! I can hear it in my sleep.
The most common place modern engineering students will run into unit conversion problems is when dealing with the International System of Units (SI) versus US customary units (USC). For Part 2 of this series, we will look at these types of unit conversion challenges from the US space program.
The Mars Climate Orbiter
Launched on December 11, 1998, the mission of the Mars Climate Orbiter was to maintain an orbit around Mars and study the Martian atmosphere and climate. This was not to be. Instead we have the most famous, and most expensive, example of a unit conversion error.
On September 23, 1999, as the Mars Climate Orbiter attempted to insert itself into its first orbit around Mars, communication was lost and was never regained. Subsequent investigation found that USC units were used in the ground software system while all other systems operated in SI units. This caused the trajectory figures to be off by a factor of 4.45 and resulted in a closer approach to Mars than expected. It is assumed that, since the orbiter was too close to the surface of the planet, heat and drag from the atmosphere destroyed the Mars Climate Orbiter.
“People make errors. The problem here was not the error. It was the failure of us to look at it end-to-end and find it. It’s unfair to rely on any one person.”
-Tom Gavin, NASA Jet Propulsion Laboratory
They failed to ‘watch their units.’ It was a $125 million mistake.
Who would think that unit conversions could be so expensive? In the case of the Constellation Program, it contributed to the cancellation of the program.
Begun in 2005, the Constellation Program was developed as a replacement of the aging space shuttle program. The focus of the program would be on manned flights with plans to return to the moon and an ultimate goal of a trip to Mars.
One of the underlying objectives of this program was the implementation of SI units across the entire program. In addition to new designs developed for the program, the ground and mission infrastructure (launch pads, test stands, etc.) that was largely developed in the 1960s for the Apollo Program would have to be updated to achieve this goal. However, it was estimated that the unit conversion costs would be approximately $370 million! In a futile attempt to support the program’s budget, it was ultimately decided to drop this plan and retain the USC units. Unfortunately, this did not save the program.
Although overall schedule and financial problems ultimately led to its cancellation in 2010, addressing units of measure is listed as one of the “Lessons Learned” in a NASA publication about the cancellation of the Constellation Program.