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

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.

He needs a PSP or something.

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!

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.)