How far does a plane travel from horizon to horizon when viewed from the ground?

[gabemcg]

I've always been curious,

Assume:

Sea level perspective

Viewed from equator

Plane flying at average cruising altitude for commercial jet

plane flying directly east to west (straight line) and goes directly overhead

nothing to obstruct view of horizon

How many miles has the plane traveled from the point where it is first visible, to the point where you can no longer see it?

 

[DrPizza]

With all those assumptions, it sounds like the problem has been well thought out... i.e. a homework question.
Then again, the most important fact is the actual altitude for the jet. 😛

So, assuming we're also going to ignore any refraction or other effects, here's a hint to start the problem:

Draw a circle, representing the earth. Draw a slightly larger circle (not to scale). Now the outer circle represents the jet's path. Draw a line tangent to the inner circle. Where that line intersect the outer circle is the limit of where you can see the plane.

Hmmm... upon thinking about it for a moment or two, I'm going to guess that the height of a person (or rather, the elevation of their eye) is going to have a relatively significant affect on the total distance. If you really want to find out, instead of a tangent line to the earth, draw two lines from eye-level that are tangent to the earth. (I'll make a diagram of both situations and post it in a minute)

 

[DrPizza]

here

That's relatively simple to solve. But, if you want to stand up instead of look at it from the surface of the earth, it's a slightly more fun problem 🙂

not drawn to scale
This one looks like it'd be a lot more fun to solve 🙂 But, alas, I have to be at a homecoming football game in 22 minutes and I haven't showered yet.

 

[blackllotus]

Originally posted by: gabemcg
Plane flying at average cruising altitude for commercial jet

I'm not sure there even is a published cruising altitude for jets. The cruising altitude can vary by more than 10,000 feet between different flights (ex: one at FL270 and one at FL400).

 

[Kyanzes]

100-150Km? But I doubt you could see that far anyway.

 

[DrPizza]

Originally posted by: Kyanzes
100-150Km? But I doubt you could see that far anyway.

He didn't say you couldn't use a pair of binoculars or something...

 

[pcy]

Hi

About 400 miles


Peter

 

[Kyanzes]

This 400 miles bothered me so I've rummaged around the net to find some calculator of the sort and to my annoyment the 400 miles seems plausable if we assume the plane is flying at 5km above sea level. Here's the link to the calculator.

 

[Calin]

If you know how far the horizon is, as seen from the plane, the distance you could see the plane is two horizons.