When and Where Will My Friend Arrive in 2011?

I have a friend who is flying from SFO to LHR on a flight that departs at 1800 (PST). We had dinner with him last night and he posed a question that he knew I would be interested in: When will he arrive in 2011? To state more clearly, when will the eastbound flight path of his aircraft intersect with the westbound path of the New Year progressing across the globe?

This kind of thing intrigues me, so when I woke up this morning at 0500 (I couldn’t sleep), I started crunching numbers. Pasted in below is the email I sent to my friend, his wife, and my wife this morning upon coming to the answer. Names have been changed to protect the innocent…

After our discussion last night at dinner, I stayed up all night doing complicated calculations of when the plane will arrive in 2011. OK, really I woke up at about 0500 and couldn’t sleep, so I pulled out my computer and started crunching numbers and maps.
The short answer to the question of when the plane will arrive in 2011 is: somewhere over Hudson Bay late in the 3rd hour of his flight.

I assumed that the aircraft will take off at 18:00 and cruise at an airspeed of 500 knots, which is about right for a Boeing 777-400, which is what Virgin Atlantic uses on most SFO-LHR flights. I also assumed a true great circle route. I didn’t include the time it takes to get up to cruising speed or flight delays….
The longer answer becomes more complicated because the border between the Central and Eastern Time Zones runs down the middle of Hudson Bay (seehttp://atlas.nrcan.gc.ca/site/english/maps/reference/national/timezones/referencemap_image_view), so it’s possible that the plane could miss the crossing from 23:59 to 00:00 entirely because of a time zone change. Rather, it’s more likely that the plane will go from about 23:45 CST to 00:45 EST by crossing the border between the two zones. This will put him in to the new year, but he will have already lost 45 minutes of it….
Because my math teacher told me that showing my work was important, here’s a spreadsheet showing the time progression in hours of flight, PST, Local Time, and UTC.
Here are the sources I used:
Great Circle Mapper – www.gcmap.com

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