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24 hour new year party.

// November 23rd, 2006 // Uncategorized

I’m going to get high this new year, literally. I’ll be at 38,000ft in a 747-400 on my way back to Malaysia from the UK. eeek! I hope there isn’t such a thing as the 2007 bug otherwise I may not be as high as I think.

Either way, this got me into a rambling conversation with my friend David in Singapore – could you fly at just the right speed to maintain your position over ‘midnight’ and therefore have a new years party that lasted for 24 hours with it being midnight the whole time?

Maths to the rescue! (complete with working for full credit)
38,000ft in miles is 7.2 miles.
The Earth’s radius is 6367 Km which is 3956.27 miles, for a total of 3963.57 miles.

Basic maths gives us the circumference of a circle is PI d. = 3.14159265 *7927.14 = 24903.844759521
Divide by 24 for miles per hour and you get 1037.660198313375 miles an hour, which, at mach 1.46 is is about 46% faster than my 747′s cruising speed.

So, given my speed of 567mi/hr, what altitude would I need to maintain in order to party for 24hrs?
(567*24)/pi gives a diameter of 4331miles which equates to approx 1790miles below sea level.

Oh well, back to the drawing board OR maybe it’s time to book my flight on a faster plane!

Update: David points out that Concorde would be able to do it.

Update 2: Edwin, another friend and colleague, points out that if I move to a higher lattitude then the distance will be shorter (clearly he’s the brains of the operation) – but that he can’t be bothered to work out what the lattitude will be. So, now I’m going to have to, otherwise I’ll never be able to sleep tonight.

Update 3: It’s about 57 degrees (North, or South). Here’s the logic…
Plane can fly at 567mph. in 24hr I can fly 13608miles (circumference, c), so what’s the radius?
c=2 *Pi * r
So c/2Pi=r
13608/6.2831853=2165.78 miles.
Minus the 7.2 miles for the altitude of the plane = 2158.58 miles.
Solving for A in sin(A)=opp/hyp
sin-1(2158.58/3956.77)=33 degrees from the pole = 57degrees from the equator
Which is basically as north as Aberdeen in the UK or 1260 miles south of Australia.
Cripes!

Update: Sian has SMS’d me to let me know that my logic is flawed – I’m assuming that the plane is at 38,oooft above the earth’s axis – not (as in reality) above the surface. back to the drawing board.