by Paul Beckwith
Early in the morning on Saturday July 6th, 2013 five locomotives and 73 tank cars carrying crude oil were parked about 12.5 km uphill (track distance) from the small idyllic Quebec town of Lac-Mégantic about 210 km east of Montreal. Apparently, the sole train engineer had finished his shift and left the train (locomotives running) a few hours earlier to get some sleep in the town; the train sat unmanned awaiting the arrival of the next engineer. Something went horribly wrong; the tank cars uncoupled from the locomotives and started rolling downhill and gathering speed as they headed towards the small town.
Map 1 (from
http://www.bbc.co.uk/news/world-us-canada-23221939 ) shows the town location within the province of Quebec in Canada and the general route of the oil train near the town. North is upward for all of the following maps.
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| Map 1 |
Map 2 below shows a satellite image from Google Earth of the town and nearby lake. The red vertical line is for scale, with a length representing a 15 km distance.
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| Map 2 |
Map 3 shows a closer-up view of the town. The dark pathway is the route of the train tracks crossing the town from west-north-west to the south-east. This Google Earth image is several years old, and rail cars can be seen at the time this image was obtained beyond the track curve towards the south-east. The train track forks into a northward and southward curving line where it crosses a major road.
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| Map 3 |
Map 4 shows an even closer view of the region. The yellow line of length 0.2 km indicates the scale. Buildings within the red zone that I outlined by freehand were leveled as the train jumped the track near the fork and plowed along the orange path. I marked red dots on the individual structures within the red zone of destruction, and counted about 40 buildings. Most of these buildings were completely leveled, with the exception of a few near the perimeter of the red zone that were severely damaged.
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| Map 4 |
Map 5 indicates the general location where the train was parked and uncoupled from the 5 locomotives, in the town of Nantes, for the shift change. This Google Earth image from 2012 has an elevation of 519 m above mean sea level on the tracks at the location where some train cars are seen in this older image. This location has the highest elevation and drops off to either side along the tracks as determined from Google Earth elevations.
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| Map 5 |
Thus, from Google Earth the elevation of Nantes is determined to be roughly 519 meters, while that of the derailment zone in Lac-Mégantic is 399 meters. From simple physics, the potential energy of the train at Nantes (PE = mgh; m=mass, g=9.81 m/s
2, h= height) was converted to kinetic energy at the derailment site (KE=0.5mv2). Solving for the speed of the train the mass cancels out giving v = sqrt(2*g*h) giving a value of 48.5 m/s (175 km/hr = 109 mph) which was clearly enough to cause the derailment if correct. This speed is an upper limit value, assuming no rolling resistance or air resistance or tank car braking. The actual number is certainly somewhat lower, but the amount is difficult to calculate exactly but we will estimate it. Assuming constant acceleration of the train down the hill, the time to reach the town after starting from rest at the top of the hill is given by t = 2x/v (x=length of track between locations = 12.5 km, v = speed at bottom of hill) gives a rolling time of 515 seconds (8 minutes, 35 seconds). The average acceleration along the track path down the hill is a=v/t=0.09417 m/s
2 (or about 0.96% of the acceleration due to gravity). Again, this is for the no friction case, modifications for friction will be estimated shortly.
Map 6 shows the route connecting Nantes to Lac-Mégantic. The rail distance is roughly 12.5 km as measured on Google Earth and indicated by the yellow lines (connecting the red point tie dots along the track), and the vertical height change is 120 meters along this path down to the derailment site. The runaway train successfully negotiated two very sharp curves. The first is at Laval-Nord (elevation 457 m, height drop from Nantes of 62 m) giving a calculated speed of 34.9 m/s (126 km/hr), a derailment here would have taken the train into forests. The second sharp curve is 0.38 km north of the lake (elevation 431 m, height drop 88 m) with a calculated speed of 41.6 m/s (150 km/hr). Failure to negotiate the second curve would have been a derailment into the forests, and would have likely spilled crude oil that would drain into the lake.
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| Map 6 |
Map 7 from this link (map
http://www.cbc.ca/news/interactives/before-after/lac-megantic/ba.html, north is down on this map) is a sliding before-and-after image that shows the buildings that were destroyed in the derailment and explosions. The after-image is also shown below. One can count 44 pancaked tank cars piled up alongside one another. The train came from the west (right side on this image which has north pointing downward) and the lead cars traveled a distance of at least 200 meters after leaving the rails. It is unclear where the other 30 or so tank cars are, presumably they still along the track behind the derailed cars (to the right on the image below).
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| Map 7 |
Some background history/information on the town can be found in this linked article: (
http://www.ctvnews.ca/canada/lac-megantic-history-of-a-picturesque-quebec-forestry-town-1.1357424 ).
Quoting from this article:
“According to the (town) website, it was one of 52 municipalities in Quebec to receive a "Four Blossoms" rating from the provincial organization "Les Fleurons du Quebec," which rewards municipalities for attractive greenery. It was also ranked among the first eight municipalities in Quebec to earn a "Carbon responsible" attestation, for climate-change measures, from the Enviro-access consulting company.”
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This award winning, climate change fighting town had no chance against the runaway oil train; which is an incredibly sad irony. Unfortunately, the train successfully negotiated two very sharp curves at speeds of 34.9 m/s and 41.6 m/s prior to entering the town of Lac-Mégantic. Derailment on either of these curves would have spared the town. In the town it derailed at roughly 48.5 m/s on a much more gradual turn crossing near or at a major road. As mentioned earlier, these speeds are upper limit speeds assuming no rolling resistance or air resistance and an on-track acceleration calculated from the basic physics of constant acceleration to be 0.96% of gravity. What is the effect of friction? If we assume a 20% reduction due to friction (rolling + aerodynamic + tank car braking) then acceleration is reduced to 0.07534 m/s
2, rolling time is increased to 576 seconds, and derailment speed is reduced to 43.4 m/s (156 km/hr or 97 mph).
Still this is an incredibly fast speed that is hard to believe. Is this ridiculous? Re-examine the images (Map 7) above of the wreck zone, and observe that for more than half the train to completely derail and pancake (>44 tank cars) required an extremely high derailment speed. Going even one step further, let us now assume that there was even more friction, for example from more hydraulic braking action on the individual tank cars, such that the total frictional acceleration reduction was reduced by 50% to 0.0478 m/s
2. Rolling time and derailment speed would respectively now become 723 seconds and 34.6 m/s (125 km/hr or 78 mph). I doubt this is fast enough to cause the level of pancaking and derailment distance observed, so my guess on the derailment speed would be between the two previous numbers. The train “black-box” should come out with accurate numbers after it is analyzed.
Given that train tank car transport of crude oil has increased by 28,000% in the last 5 years (
http://www.huffingtonpost.ca/2013/07/07/lac-megantic-explosion-oil_n_3558647.html ) without a corresponding increase in safety inspections (and even cost cutting reductions) it is virtually certain that the frequency of accidents will increase. Pipelines are no answer to transporting oil, given that we are undergoing abrupt climate change. In fact, increases in the frequency, severity, and geographical regions of extreme weather events due to jet stream behavior completely changing due to rapid climate change is also greatly increasing the risk of oil transport by rail and pipeline from flooding, drought, heat waves, and extremely large temperature swings over short periods of time. In fact all infrastructure is being severely compromised by extreme weather. As the people in Calgary, Toronto, India, Europe, and many other places around the world are discovering first hand.
Paul Beckwith is a part-time professor with the laboratory for paleoclimatology and climatology, department of geography, University of Ottawa. He teaches second year climatology/meteorology. His PhD research topic is “Abrupt climate change in the past and present.” He holds an M.Sc. in laser physics and a B.Eng. in engineering physics and reached the rank of chess master in a previous life.
