Strange Word Problem One

[TromboneAl]

I need to figure out some things for a book I'm writing. The first question is the easy one:

If I'm standing on a level plain, and an airplane flying at 40,000 feet passes, leaving a contrail, what's the maximum distance at which I could see it?

The easy answer comes from calculating the distance to the horizon when at 40,000 feet, and that answer is: 245 miles.

I've read that "dust and water vapor in the air will rarely let you see more than 12 miles," but I know I've seen snow on the Sierra Nevada mountains from Mt. Diablo in the Bay Area, and that's a distance of at least 180 miles.

So I'm guessing 200 miles is a good answer. Thoughts?

 

[REWahoo]

I think 125 -150 miles might be more accurate, and even that might be a stretch. On a clear day the sky overhead maybe blue but the dust and water vapor you mentioned makes the sky appear to "white out" as your line of sight nears the horizon. Since the contrail is also white, I doubt you can actually see it as far away as is theoretically possible.

 

[braumeister]

I think 125 -150 miles might be more accurate, and even that might be a stretch.

+1
Also, are you talking line of sight distance, or how far along the surface of the Earth?
I would think about 200 miles would be the max practical LOS distance for the reasons REWahoo mentioned.

 

[samclem]

So I'm guessing 200 miles is a good answer. Thoughts?

I think that's about right. I recall seeing contrails from missile launches from Vandenberg AFB from my home east of LA, and those locations are 200 miles apart. I know the missiles were launched over the water (away from my location), so the contrails I saw at altitude were more than 200 miles away from my location.
Given the right lighting (e.g. sun below the observer's horizon but illuminating the contrail at altitude), they can really stand out from the sky. The ones I saw could well have been above 40K feet, but as you point out in your OP, there's no curvature of the earth restriction to seeing something out to 245 miles (assuming a cue-ball earth, which only holds true over water or very flat terrain--otherwise it can be longer or shorter).

 

[TromboneAl]

OK, thanks. On to problem two.

 

[splitwdw]

Are you standing in a plane as the other plane passes? In the cockpit or window seat?

 

[Meadbh]

And do you have enough fuel?

 

[drb391]

assuming the horizon ts 12 mi (I've heard), can't you use the pythagorean theorem?

 

[Bestwifeever]

Will Lena be on the plane or on the mountaintop?

 

[splitwdw]

Will Lena be on the plane or on the mountaintop?

and will someone be vomiting?