How far away are aircraft?

[moleamol]

On these fine clear days that we have been having, you see all sorts of aircraft very high in the sky, leaving contrails. Say there was one at 30 degrees from the ground as you look forward, cruising along in the distance (assuming it's a commercial airliner). How far away, in miles along the ground would that be?

[RobM77]

That's simple trigonometry. Planes fly at about 10,000 metres I think, so if it's at 30 degrees then that's 20km on your line of sight, and 17.3km along the ground.

Edited to say: I misread your question. In miles along the ground that's just under 11 miles.

Edited by RobM77 on Saturday 17th May 17:28

[bobt]

depends how long the conveyor belt is!

[_James]

What about the curvature of the earth? Surely that affects it.....

[Mars]

SOH, or

Sin(A) = Opp / Hyp, or

Hyp = Opp / Sin(A)

Hyp = 10,000 / Sin(30) = 20,000


Rob's reply was more elegant.

[moleamol]

RobM77 said:

That's simple trigonometry. Planes fly at about 10,000 metres I think, so if it's at 30 degrees then that's 20km on your line of sight, and 17.3km along the ground.

Well that's what I thought at first, but then I thought well how far away is the sky. The way you can watch an aircraft come into sight on the horizon, then watch it all the way across the sky and disappear behind the other horizon really confused me. How far away would it be as it came into sight on the horizon?

[dilbert]

I think it depends how far away they are!
Try Supersonic SONAR/RADAR, maybe that will help you.

Edited by dilbert on Saturday 17th May 17:38

[dilbert]

moleamol said:

RobM77 said:

That's simple trigonometry. Planes fly at about 10,000 metres I think, so if it's at 30 degrees then that's 20km on your line of sight, and 17.3km along the ground.

Well that's what I thought at first, but then I thought well how far away is the sky. The way you can watch an aircraft come into sight on the horizon, then watch it all the way across the sky and disappear behind the other horizon really confused me. How far away would it be as it came into sight on the horizon?

Now I'm really confused!

[Jack Pearson]

The Lancaster Bomber did a flyby over my house earlier in Daventry

Fack me sideways that thing is loud!

[moleamol]

dilbert said:

moleamol said:

RobM77 said:

That's simple trigonometry. Planes fly at about 10,000 metres I think, so if it's at 30 degrees then that's 20km on your line of sight, and 17.3km along the ground.

Well that's what I thought at first, but then I thought well how far away is the sky. The way you can watch an aircraft come into sight on the horizon, then watch it all the way across the sky and disappear behind the other horizon really confused me. How far away would it be as it came into sight on the horizon?

Now I'm really confused!

Ok, if it came into sight directly in front of you, and crossed over your head and went out of sight directly behind you.

[RobM77]

moleamol said:

RobM77 said:

That's simple trigonometry. Planes fly at about 10,000 metres I think, so if it's at 30 degrees then that's 20km on your line of sight, and 17.3km along the ground.

Well that's what I thought at first, but then I thought well how far away is the sky. The way you can watch an aircraft come into sight on the horizon, then watch it all the way across the sky and disappear behind the other horizon really confused me. How far away would it be as it came into sight on the horizon?

The horizon is about 20 or 30 miles away I think under average seeing conditions for a six foot tall man. If you want to visualise it draw a curved line to represent the earth (or in your case, the space on the earth the UK occupies). Then draw you standing up and a straight line for your line or sight. Obviously a plane appearing will be more than 20 or 30 miles away is it's over ground you can't even see (in fact from my calculations above, a plane cruising at 10,000 metres at 30 degrees visual elevation is actually directly over the limit of your horizon vision; a nice coincidence!).

If you want the exact distance from first sight to last sight then an interesting exercise would be to time a plane from appearance on one horizon until it's dissapearance on the other. Find out the cruising speed of a plane (a 747 is about 555mph), and work it out from that. So, if it takes half an hour from when you first spot it to when you see it vanish again then it's flown 227.5 miles in that time. That's assuming it's cruising that is and not taking off. Over Britain I'd have thought most planes would be climbing and descending, which complicates things even further!

[theaxe]

An interesting and semi-relevant fact I heard is that if an aircraft appears larger than your thumb when at arms length, then it's close enough to bring down with small-arms fire (the aircraft, not your thumb).

Not very useful but interesting none the less.

[GBGaffer]

RobM77 said:

The horizon is about 20 or 30 miles away I think under average seeing conditions for a six foot tall man.

Try a tenth of that and you would be nearer the mark. A height of eye of 5' at sea level gives you a horizon distance of approx 2.7 miles.

Cheers

Graham

Edited by GBGaffer on Saturday 17th May 18:29

[RobM77]

GBGaffer said:

RobM77 said:

The horizon is about 20 or 30 miles away I think under average seeing conditions for a six foot tall man.

Try a tenth of that and you would be nearer the mark. A height of eye of 5' at sea level gives you a horizon distance of approx 2.7 miles.

Cheers

Graham

Edited by GBGaffer on Saturday 17th May 18:29

Sorry, you're dead right:

http://science.howstuffworks.com/question198.htm

I got my figures from another website, which is clearly unreliable!!

[Skywalker]

dilbert said:

I think it depends how far away they are!
Try Supersonic SONAR/RADAR, maybe that will help you.

Edited by dilbert on Saturday 17th May 17:38

I don't know if his wings are enough like a shield of steel to allow him to cope.

[Hedders]

GBGaffer said:

RobM77 said:

The horizon is about 20 or 30 miles away I think under average seeing conditions for a six foot tall man.

Try a tenth of that and you would be nearer the mark. A height of eye of 5' at sea level gives you a horizon distance of approx 2.7 miles.

Cheers

Graham

Does it follow then, that if you were ten foot tall you would see 5.4 miles or is there a curve?

[dilbert]

Skywalker said:

dilbert said:

I think it depends how far away they are!
Try Supersonic SONAR/RADAR, maybe that will help you.

Edited by dilbert on Saturday 17th May 17:38

I don't know if his wings are enough like a shield of steel to allow him to cope.

[GBGaffer]

Hedders said:

Does it follow then, that if you were ten foot tall you would see 5.4 miles or is there a curve?

No, at 10' the horizon would be roughly 4 miles away, and yes, there is a curve - the Earth is a sphere (Unless you are a member of the flat Earth society)

[Dr Jekyll]

To put it another way, at 40,000 FT the horizon is around 245 miles away. So given clear weather and a good pair of binocs that's theoretically how far away you can see the aircraft from the ground.

[moleamol]

Dr Jekyll said:

To put it another way, at 40,000 FT the horizon is around 245 miles away. So given clear weather and a good pair of binocs that's theoretically how far away you can see the aircraft from the ground.

That's much closer to what I was thinking.