Nate Holt's Blog

July 5, 2009

How much lighter is an east-bound 747?

Filed under: Musings — nateholt @ 9:03 am

(note: this was originally posted in April 2006 on the old blog)

My last long trip… center seat, coach, with every seat covered. If I want to open my PC’s screen enough to see it clearly, I have to move it so close that I can barely type. If I want to push the PC out to where I can more comfortably type, I have to close the screen way down so it can fit between the tray table and my front neighbor’s max reclined seat. Choice is a) see screen but can’t type, b) type but can’t see screen. Was not a happy time.

Mind wanders, trying to find something to latch on to for awhile to somehow speed up the passage of time. Need sudoku.

Okay, try to think about this… how much lighter is a 747 flying east than flying west? Is there a difference and might it be measurable? Gather known facts. Earth is about 4000 miles in radius which works out to about 25000 miles around at the equator. It rotates in 24 hours, so the rotational speed at the equator has to be around 1000 miles per hour in the eastern direction (sun appears to rise in the east since the earth is rotating in that direction). A fully loaded 747-400ER has a max take-off weight of 910,000 pounds (make it a million). Put cruising speed at around 600 mph.

So, two identical 747’s, fully loaded, both at cruising speed, pass each other over Singapore (on the equator). The first 747 is flying due east, the other flying due west. How much “lighter” is the east-bound 747 than its identical twin flying west?

With the earth’s 1000 mph rotational speed at the equator added in, the east-bound 747 is “spinning” around the globe at 1600 mph to the east. The west-bound 747 is working against the 1000 mph eastward spin of the earth, so the net “spinning” speed for it is only 400 mph.

Could a 1200 mph rotational speed difference be enough to register a measurable “weight” difference?

Donno. Think about the extreme case. How fast would a 747 have to be spinning around the globe in order to have its “weight” drop to zero? It happens with anything put into orbit. From grade school days, us kids learned that astronauts would orbit the earth every 90 minutes or so. In low earth orbit, it’s probably a bit more than 25000 miles to get around the globe. Doing it in 90 minutes works out to about 17000 mph. So if we could get our 747 up to 17000 mph, we’d either break apart or we’d experience a 100% reduction in “weight”.

What about the 1600 mph versus 400 mph for the passing 747s along the equator? The calculator here gives the difference in centripetal acceleration for the different speeds around the 4000 mile radius earth. According to the calculator, the 1600 mph 747 would experience a 0.0081G negative acceleration and the 400 mph 747 a 0.0005G negative acceleration. Multiplying the difference by the million pound weight of the fully loaded aircraft yields a “weight” difference of 7600 pounds.

Seems like a lot. Could this be right?

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