[Guest]

An airplane flies in a straight line from airport A to airport B, then back in a straight line from B to A. It travels with a constant engine speed and there is no wind. Will its travel time for the same round trip be greater, less or the same if, throughout both flights, at the same engine speed, a constant wind blows from A to B?

Please use spoilers, and explain your answer.

[bonanova]

fastest with no wind.

Upwind flight adds more transit time than downwind flight gives back.

You can't average speeds by distance.

Consider the case of a headwind greater then the airspeed of the plane.

It's also true in the case of a side wind.

[Guest]

If there is a wind factor, regardless of where it is blowing to, it will be counterproductive.

How?

Well, consider that:

the plane flies at velocity V

the wind blows giving an advantage of W (and -W on the return flight)

the traveled distance is D

With no wind, the time unit you take to travel from A to B, is T (call it a n hour, minute, second, day... whatever you like)

So, at no wind:

D/V + D/V = 2T

Thus, with a wind blowing:

= D/(V+W) + D/(V-W)

= [D*(V-W) + D*(V+W)]/[V^2 - W^2]

= [DV - DW + DV + DW]/[V^2 - W^2]

= 2DV/[V^2 - W^2]....................(1)

Since the denominator is being afected by the wind factor, making it a smaller number, the total value for the fraction will increase, hence:

2DV/[V^2 - W^2] > 2T

Check it out for W = 0

2DV/[V^2 - W^2]

= 2D/V...............................(2)

Comparing (1) and (2) :

2DV/[V^2 - W^2] > 2D/V

2DV^2 > 2DV^2-2DW^2

It's time we're talking about here, so yes... having a wind of any kind will take the round trip longer, assuming the wind remains constant during all the trip.

Edited January 19, 2011 by jagdmc

[wolfgang]

If the earths rotation will be concidered,so there will be a great difference between them.

i.e. with earth rotation or against earth rotation.

[Guest]

Wolfgang,

I don't think that the effect of earth rotation is the same as the wind effect. In one direction the earth velocity is increasing your speed, but the destination is moving away from you at the same speed. In the other direction, the earth velocity is decreasing your speed but the destination is moving toward you at the same speed. So earth velocity does create a difference in time, like wind does.

I would put this in a spoiler, but I can't figure out how to use it. The spoiler window seems to be stuck off to the left of my screen and I can only see a small part of it.

[Guest]

Actually I meant to say earth rotation DOES NOT make a difference in round trip time.

[Guest]

Bonanova and jagdmc have got it. Great job!!

And, autonav, you can just manually type the spoiler tags (that's what I do).

[spoiler]<insert text here>[/spoiler]

[wolfgang]

Wolfgang,

I don't think that the effect of earth rotation is the same as the wind effect. In one direction the earth velocity is increasing your speed, but the destination is moving away from you at the same speed. In the other direction, the earth velocity is decreasing your speed but the destination is moving toward you at the same speed. So earth velocity does create a difference in time, like wind does.

I would put this in a spoiler, but I can't figure out how to use it. The spoiler window seems to be stuck off to the left of my screen and I can only see a small part of it.

But if you read the question,you`ll see that there is(NO)wind.

[wolfgang]

Bonanova and jagdmc have got it. Great job!!

And, autonav, you can just manually type the spoiler tags (that's what I do).

[spoiler]<insert text here>[/spoiler]

but why?!!

you said "there is no wind".

[Guest]

I think you are reading the question wrong...

An airplane flies in a straight line from airport A to airport B, then back in a straight line from B to A. It travels with a constant engine speed and there is no wind. Will its travel time for the same round trip be greater, less or the same if, throughout both flights, at the same engine speed, a constant wind blows from A to B?

[Guest]

as the plane jet engine get its forward velocity when it throgh air backward, while moving a to b and air in same direction it will effect will be neglgible , ie plane get forwardedd byy win , but littel bit effect the working of jet , but for journey of btoa itts net velocity increse a lot more than wind resistance, so time taken will be lass

An airplane flies in a straight line from airport A to airport B, then back in a straight line from B to A. It travels with a constant engine speed and there is no wind. Will its travel time for the same round trip be greater, less or the same if, throughout both flights, at the same engine speed, a constant wind blows from A to B?

Please use spoilers, and explain your answer.