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Round Trip Flight: Newsletter Challenge (05/17/05)

Posted May 17, 2005 7:00 AM

The question as it appears in the 05/17 edition of Specs & Techs from GlobalSpec:

You return home from a recreational flight (your friend has a small 4-seat plane) to find your two kids quarreling yet again. As you get the gist of the conversation you determine they are "discussing" a round-trip flight to a local neighboring airport, normally requiring an hour in still air. Your son has asked what happens to the round-trip time if the wind is blowing against you on the way out; your daughter says, "Idiot, it takes longer because of the headwind on the way out but you make up the time on the return trip with a tail wind. So it still takes an hour." Your son responds in his normal mature way, "Jerk! It does not!" "Does, too, twerp!" replies your daughter. "No it doesn't, blockhead!" responds your son. You interrupt this loving exchange with an "Ahem..." Then what do you say?

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The Feature Creep

Join Date: Feb 2005
Location: Boston, MA
Posts: 1055
#1

Avoiding the jet stream.

05/17/2005 8:42 AM

I just came back from a European trip and our flight took a much further northern track to avoid going into the jet stream the wrong way.

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The Engineer
Engineering Fields - Engineering Physics - Physics... United States - Member - NY Popular Science - Genetics - Organic Chemistry... Popular Science - Cosmology - New Member Ingeniería en Español - Nuevo Miembro - New Member

Join Date: Feb 2005
Location: Albany, New York
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#2

This kid is getting annoying

05/17/2005 3:07 PM

He needs a PSP or something.

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Active Contributor

Join Date: May 2005
Posts: 17
Good Answers: 1
#3

Round Trip

05/17/2005 9:11 PM

Ha, The trip always takes longer when there is wind. In fact, if the wind is equal or faster than the plane then you'll never get there! Well, you could wait to be blown around the earth.... The equation goes something like this, with D=Distance, P=plane speed, W=Wind speed: round_trip_time=D/(P-W)+D/(P+W), or reduced: time=2DP/(P^2-W^2) Asymptotic behavior as the wind speed approaches the plane..... Hugh PS--I would have liked to have seen the girl with the correct answer in the problem; too many wise guys and not enough wise girls in engineering!

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Friend of CR4

Join Date: Dec 2004
Posts: 1995
Good Answers: 35
#4

And the Answer is....

05/24/2005 12:05 PM

As written in the 5/24 issue of Specs & Techs from GlobalSpec:

Well, your son is right on this one. You can never make back the time lost due to a headwind (assuming constant power setting in both directions). One way to see this is to perform the following thought experiment. Assume the normal round-trip time in still air is an hour, and assume the headwind is equal to the max speed the airplane can go at full power. In this situation, the plane simply stands still with respect to the ground and it takes "infinite" time to get to the destination. If the wind is just a little bit slower than the max flight speed, it takes "a really long time" to get there. Of course, the return trip is pretty quick but that "really long time" has been used up on the trip out. The round-trip time is still "really long" in this situation. Compare this with the still air scenario of an hour round-trip and you can see that any headwind at all is going to cost you some time on the round-trip. (This is why it really pays to be able to go fast in a commercial setting — the more capable your plane is of going fast as compared with any foreseeable headwind, the better able you are to make an on-time arrival.)

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