The Mars Climate Orbiter: A Multimillion Dollar Mistake
The Story
Grossman (1999) addresses the incident of NASA’s Mars Climate Orbiter in her article named “Metric Math Mistake Muffed Mars Meteorology Mission”. She explains how a simple unit conversion mistake caused the Orbiter to burn up in the Martian atmosphere. The vessel costed NASA a whopping $125 million when it vanished into the Martian atmosphere. The problem, later identified by a NASA review board, owed to a software glitch. The software was used to calculate the thrust in “pounds of force” while the other software took the input in “newtons”. This happened due to the fact that Lockheed Martin (the builders of the vessel) expressed force in pounds while NASA does it in newtons. The change in force, caused by the input in pounds instead of newtons, multiplied the force by a factor of 4.45 (as 1 lb. force = 4.45 Newton). As a result, the vessel ended up too close to the Martian atmosphere and eventually vanished.
The Application
Since 1 mile = 1.609 kilometers, then 35 miles = 35 x 1.609 = 56.315 kilometers.
This means that the orbiter ended up about 56 kilometers from the Mars surface while it was supposed to stop about 150 kilometers. Therefore, the orbiter ended up about 94 kilometers off its target distance.
Even if the orbiter could go as close as 85 kilometers from the surface of Mars, it would still not be able to function because it ended up at a distance of 56 kilometers from the surface. Therefore, the minor negligence in unit conversion costed NASA a fortune.
Disneyland Tokyo: A Bumpy Blunder
The Story
JoeInJpn (2004) provides the report of the Tokyo Disneyland Space Mountain rollercoaster incident on December 5, 2003 (Kyodo, 2003). The rollercoaster derailed due to the breakage of the axle of the ride’s rear wheels. The cause of the axle breakage was found to be the excess gap between the axle screw nut as compared to the design specifications. The gap caused excessive vibrations causing more stress on the axle nut than it could bear and ultimately the axle broke. It was later found that the excess gap owed to a change in the design specifications of the size of the axle bearing. The design specifications of the axle bearing were changed from inches to millimeters in September 1995 and the axle diameter was subsequently changed to 45 mm from 44.14 mm. Due to this change, there were two drawings present at the same time with different diameters. The drawing with wrong specification (i.e. 44.14 mm diameter) were negligently used to order that caused the issue. This negligence caused the gap in the axle bearing to be over 1 mm where it was supposed to be about 0.2 mm according to the design.
The Application
The thread diameter of the bolt of 1.75 inches in millimeters is calculated as follows.
Since 1 inch = 2.54 centimeters and 1 centimeter = 10 millimeters, then 1 inch = 25.4 millimeters
So, 1.75 inches = 1.75 x 25.4 millimeters = 44.45 millimeters.
Therefore, the diameter is 44.45 millimeters.
If the order was mistaken for 1.75 centimeters instead of 1.75 inches, then the error will be calculated as follows.
1.75 inches = 44.45 millimeters
1.75 centimeters = 1.75 x 10 millimeters = 17.5 millimeters.
Therefore, the error in the bolt would be 44.45 – 17.5 = 26.95 millimeters.
Air Canada Flight 143: Unit-Caused Fuel Shortage
The Story
Airplanes carry an optimum amount of fuel, including the safety factor, such that they can complete the journey safely without carrying an excessively unneeded amount of fuel. This is because of the fact that excessive fuel means excessive weight which, in turn, increases the fuel consumption of the aircraft. For this purpose, an electronic gauging system is employed. Unfortunately, the electronic gauging system on Air Canada Flight 143 was not working properly when the airplane was headed to Edmonton from Ottawa on July 29, 1983. Due to the malfunction of the electronic system, the pilots of the plane had to carry out the fuel calculation manually with special “drip sticks”. The pilots supposedly took the measured weight of the fuel in kilograms while the actual weight was in pounds. This misconception happened because most new airplanes employ the metric system while the ones in United States still measure in British units. Since, one kilogram is equal to 2.2 pounds, the calculated amount of fuel was about 2.2 times more than the fuel that was actually present. The aircraft ran out of fuel, while still in the air, and an emergency landing was made at the Gimli field, courtesy the knowledge of the copilot because of his training in the Canadian Air Force earlier (Witkin, 1983).
The Application
The pilot calculated the fuel requirement for the trip to be 22,300 kilograms. The amount of fuel that was present in the tanks was 7,682 liters.
Since one liter of jet fuel weighs 0.803 kilograms, therefore the mass of fuel present in the tanks would be approximately 7682 x 0.803 = 6168 kilograms.
The additional fuel required to complete the trip would therefore be 22300 – 6168 = 16132 kilograms.
The Miscalculation of the Circumference of the Earth by Chris Columbus
The Story
McCormick (2012) explains how Christopher Columbus erred in his calculations of the circumference of the earth. Christopher Columbus thought, due to his miscalculation, that he could reach the Indies if he sailed west across the Atlantic. He, being optimistic, used the values provided by Abu al Abbas Ahmad ibn Muhammad ibn Kathir al-Farghani (also known as Alfraganus) who was a Persian geographer. Alfraganus proposed that one degree at the equator was equal to 56.67 miles. The error that Columbus committed was that he assumed Alfraganus to be using the Roman mile while he was actually using the Arabic mile. The Roman mile is equal to 4856 feet while the Arabic mile is 7091 feet. Therefore, a difference of 2235 feet was induced into his calculations unknowingly, shortening the distance by a great deal. This shortening of the distance caused Columbus to think that he would easily be able to reach the indies. These calculations were based on the calculations for the circumference of the earth completed by other scholars in the past. In fact, he did reach the “New World” but because of his optimism, and not his calculations.
The Application
The distance from Charleston SC to Nassau, Bahamas directly is 556 miles (Google Maps, 2016).
The steps to convert this distance into nautical miles and Roman miles are given below.
Since 1 Nautical mile = 1.15 miles, therefore, 556 miles = 556 / 1.15 = 483 Nautical miles.
Similarly, 1 Roman mile = 0.92 miles, therefore, 556 miles = 556 / 0.92 = 604 Roman miles.
So, the distance from Charleston SC to Nassau, Bahamas is approximately 483 Nautical miles or 604 Roman miles.
References
Google Maps. (2016). Charleston, South Carolina, USA to Nassau, The Bahamas. Retrieved from https://www.google.com/maps/dir/Charleston,+South+Carolina,+USA/Nassau,+The+Bahamas/@28.8376345,-83.1369676,6z/data=!3m1!4b1!4m13!4m12!1m5!1m1!1s0x88fe7a42dca82477:0x35faf7e0aee1ec6b!2m2!1d-79.9310512!2d32.7764749!1m5!1m1!1s0x892f7c99b981dbc9:0x2aef01d3485e50d2!2m2!1d-77.355413!2d25.0479835
Grossman, L. (1999, November). Metric Math Mistake Muffed Mars Meteorology Mission. WIRED. Retrieved from https://www.wired.com/2010/11/1110mars-climate-observer-report/
JoeInJpn. (2004). OLC: Space Mountain Accident Report Released. Retrieved January 7, 2017, from http://www.mouseinfo.com/forums/tokyo-disney-resort/13134-olc-space-mountain-accident-report-released.html
Kyodo. (2003, December 6). Disneyland roller coaster derails. The Japan Times. Chiba, Japan. Retrieved from http://www.japantimes.co.jp/news/2003/12/06/national/disneyland-roller-coaster-derails/#.WHDK-lV9671
McCormick, D. (2012, October). Columbus’s Geographical Miscalculations. IEEE Spectrum. Retrieved from http://spectrum.ieee.org/tech-talk/at-work/test-and-measurement/columbuss-geographical-miscalculations
Witkin, R. (1983, July 30). JET’S FUEL RAN OUT AFTER METRIC CONVERSION ERRORS. The New York Times. Retrieved from http://www.nytimes.com/1983/07/30/us/jet-s-fuel-ran-out-after-metric-conversion-errors.html
