Tuesday, December 05, 2006

Difficult Puzzle

Here's a new puzzle. It's not easy. And it lures people into an incorrect answer. We'll see if Dr. Kim has ever used this one for his class.

For a round-trip flight between New York and Los Angeles and back to New York, how will a constant and uniform wind affect the total elapsed time of the flights compared to having no wind? Will a constant wind, uniform across both legs of the trip, make the total flight time longer, make it shorter, or have no effect?


Joe said...

Hmmm. Let's see:

NY to LA
Flying into/against prevailing westerlies (head wind) will slow the plane down.

LA to NY
Flying with the prevailing westerlies (tail wind) will increase speed along with the jet streams

Tail wind defined as wind that assists the intended progress of an exposed, moving object

Jet stream defined as high speed air flow in the atmosphere forming air rivers several hundred miles across that generally move west to east and mark the boundary that separates two global air masses with significant differences in temperature.

So, my understanding is that the prevailing winds blow from west to east, so when we are traveling east, we get a speed gain, and when we travel west, we get a speed penalty.

There is also the jet stream that flows eastward, further speeding up the aircraft.

When landing/taking off you must always go against the wind. This may add time to your approach, which is one of the slowest parts of the flight.

Now, because this is a difficult puzzle, please tell me why I'm wrong.

And, all this talk about flights makes me want to fly somewhere...

Joe said...

Ooops, forgot my answer: In summary, the best wind is no wind at all. This is because you spend more of the flight in the headwind than the tailwind. I didn't do the math to prove.

Dr. Kim, the Aero guy said...

I like to look at limiting cases. Suppose the steady wind were axactly the same speed that the airplane could fly. Then the trip in one direction would take half the normal time, but the trip in the other direction would take infinity. You'd just sit there going nowhere. So the total trip will take longer when there's a wind versus no wind. So, yeah, I agree with Joe.

Dr. Kim, the Aero guy said...

Oh, no I never used this is my class on aircraft performance and dynamics.

Anonymous said...

Well Played, Dr. Kim. I got the same result, but didn't think to take it to the limit like you did, which was pretty bright. I actually had to write this one out. PS--as an annoying side note I'd like to see the "constant wind" be phrased with velocity, because at first I thought it was tricky, what with Mike's comment.

matthew said...

Let's drop the LA/NY thing. Go with A and B as I don't think it really matters. The flight between A and B with any wind but a head wind means setting a course for point C. For example, if the A and B were west and east respectively and the wind was coming from the north, point C would be north of point B. Essentially you're correcting for drift.

A, B and C define a right trangle, ABC. AC > AB. Without wind, flying AB takes t1 and flying AC takes t2. t2 > t1. With a wind, flying AB takes t2. So with any wind but a head wind, your flight is longer. I think you can go a step futher and say while the windy version is longer, both legs are of equal length.

With a head wind on one leg and a tail wind on the other your flight length is still longer. Here's the example I used:

100 miles between a and b, flight speed 100mph.
without wind
leg 1: 1 hr
leg 2: 1 hr
total 2 hrs.
with 10 mph wind wind
leg 1: effective speed 90mph
100/90 hr, or 10/9 hr, or 110/99 hr
leg 2: effective speed 110mph
100/110 hr, or 10/11 hr, or 90/99 hr
total 200/99 hr which is longer than 2 hours

Unless I'm totally misguided, your flight is always longer.

matthew said...

...wait a sec, this doesn't have anything to do with flatulence and matches? Because that flight will most definately be longer...