Estimating the speed of the plane.
I’m sometimes bored while flying, and I like looking out the window (though if I can, I usually pick aisle seats so I can exit more quickly).
I realized something rather amusing. I closed one eye, and held two fingers about an inch apart and a foot away from my open eye. Then, I timed how long it took an object on the ground to move from the one finger to the other finger an inch away; it took about ten seconds.
Let 
be the distance in feet from my eye to that point on the ground. By similar triangles, moving an inch when one foot away from my eye means moving inches on the ground. The distance from my eye to the ground is (wild guess!) 60,000 feet, so the point on the ground actually moved 60,000 inches, or 5000 feet, about a mile. Moving a mile in ten seconds is moving six miles per minute, or 360 miles per hour.
I seem to recall that 450 mph is actually how fast a commercial jet might go, so at least I’m within an order of magnitude. Now 450 miles per hour would have been 39,600 feet per minute, or 6600 feet in ten seconds, or 79,200 inches in ten seconds, so maybe I should’ve estimated 80,000 feet to the ground. But there are so many other sources of error in this technique…
Are there other fun things to estimate when trapped on a plane?
Posted: January 16th, 2007 under Physics.
Comments: 2
Comments
Comment from Anna
Time: January 18, 2007, 7:12 pm
I have done the very same thing on an airplane. I thing cruising altitude is about half that, but then one has to take into account the angle one views it at…blech. Of course, slower airplanes also fly at lower heights…
I tried estimating the distance around the earth when I was smaller, using the following approximations: 1) there is a 6 hour time difference between Toronto and and Amsterdam 2) it takes about 7 hours to fly toronto-Amsterdam 3)It takes circa three hours to go from Winnipeg to Toronto 4) it would take about three days of driving to do that.
Not terribly accurate..
Comment from Anna
Time: January 18, 2007, 7:28 pm
Oh, wait, no, it is! A driving day is c. 8 hours, so a plane goes 8* as fast, i.e. 800 km/hr. For 7 hrs, this is 4800 km, which we’ll round up to 5000 (because both the speed and time are a wee bit low). Now, all this is going on at latitude 45 degrees or so. Thus the equatorial distance is 10000 km. Then the whole circumference of the earth is 400000 km (because the time difference tells us we’re at a quarter of the earth). Cool!
It didn’t work as a kid because I didn’t know how to factor in the fact that you’re not at the equator—though I knew it made a difference.
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