PDA

View Full Version : Back of a cigarette packet calculation help

SpringHeeledJack
5th Jan 2009, 19:14
I was sitting a few days ago in western Ireland looking out into the Atlantic when a flyover flewover on it's way to the US of A. It was a crystal clear day and the contrail could be seen for a considerable amount of time until it merged with the horizon. The people that I was with were guessing how far away it was from us at that point. My guess was 200 miles.

I have tried to calculate this in my head today, but not having a pencil and paper to hand this has proved difficult. This is where the brilliant and jaded minds of the jet-blastians are needed... :)

Assuming that the aircraft was at 11,300m (approx 37,000 feet), what was the approximate down-range distance ? If it were flying at sea-level then my guess would be approximately 12 miles :8

regards

SHJ

btw Happy new year!

Bushfiva
5th Jan 2009, 19:45
Back of envelope, 384.3 km

kangaroota
5th Jan 2009, 19:59
You have an envelope 384.3 km long?:confused:

FlightTester
5th Jan 2009, 20:18
Good guess at 200NM.:ok: Using SQRTof 37000*1.22, or SQRT(1.5*37000) (either ones a good calculation to find the horizon distance) I come up with 234NM or 235NM respectively.

Chesty Morgan
5th Jan 2009, 20:19
The simple formula for straight line distance to the horizon is:

Sq Root of 1.5 x h (where h is height in feet)

So if you take the height of the airliner minus your height above sea level, and for arguments sake you are 300ft above sea level and multiply it by 1.5 you get...umm...55050. The square root of that is approximately 235 nautical miles.

For observers on the ground or sea level with eye height at h = 5 ft 7 in (5.583 ft), the horizon appears at a distance of 2.89 miles.

Edit: Ha! Beaten by a minute...harrumph!:ok:

ExSp33db1rd
5th Jan 2009, 20:40
Reminds me of the contest I had - at \$2 a go - to work out when the sun would pop up over the horizon heading East on a night flight, working out relative longitudes, Sunrise / Sunset tables, ETA, Ground Speed, and aircraft height needed a little more than the back of a fag packet, and of course I didn't admit to the cunning formula I had laboriously worked out some time before, so usually managed to win enought to buy my first beer at destination ! many fights with the ( usually ) Flt. Eng. if the horizon was obscured by low cloud !

All started one day when the cabin crew asked when it would get light, to plan their breakfast service for awakening passengers, how the Hell do I know, about 2 hours before arrival I guess ? but it got me thinking, hence the above.

707 Captains realised that there were 10 nuts holding the nosewheel in place, counting clockwise from the tyre valve they would sell numbered nuts to the 10 crew we carried, and the one whose nut was nearest to the ground scooped the pool. Cabin Crew accused the Flt. engineer of being in cahoots with the ground crew man holding the chocks ! ( he probably was, too ! )

All good fun.

bnt
5th Jan 2009, 22:13
Another way is to imagine (or draw) a very big triangle, with three points: you, the plane, and the centre of the earth. If we assume that you were at sea level, then you are on the horizon as seen from the plane, and so the angle at your point is 90°. With that, it's not hard to work out the lengths of the sides of the triangle:

One leg of the triangle is the distance from you to the centre of the Earth = the radius of the Earth, which is about 6365 km at that latitude (53°), according to the chart on Wikipedia (http://en.wikipedia.org/wiki/Earth_radius). (You can calculate a more exact figure if you want, using the formula there.)
The 2nd leg, from the plane to the centre of the Earth = 6365 + 11.3 km = 6376.3 km
We can work out the 3rd leg, from you to the plane, if we use the Pythagoras theorem: distance = √( 6376.3² - 6365²) = 379.4km or 235.7 miles.(You could subtract your height above sea level from the height of the plane, though that introduces a tiny error, since "up" at your location is not quite the same as "up" at the plane's location: there's an angle in between that makes a little difference to the figures.)

G-CPTN
5th Jan 2009, 22:24
Congratulations to bnt - such a simple and understandable solution that can (almost) be worked out without prior knowledge (apart from general knowledge). :ok:

Gordy
6th Jan 2009, 00:44
bnt had the right way to do it. The fromula is actually 1.23 X square root of your height in feet. This will give "slant range" in nm. Therefore @ 37,000 feet he would be 236nm away.

Bronx
6th Jan 2009, 00:56
So the "right" way to do it gives 236 nm
whilst the other ways give 234 nm, 235 nm and approximately 235 nm.

And the height of the airplane is a guess anyways. :)

B.

Howard Hughes
6th Jan 2009, 07:12
We always played guess the fuel burn to the exact pound!:eek:

Of course having control of both the throttles and the tiller once on the ground, helped one guess the exact burn on a number of occasions. Having calculated a cunning formula, it was only those fecking ATC'ers that could stuff it up!;)

tony draper
6th Jan 2009, 07:45
Are you people trying to say the Earth is round?:uhoh:
Hmmm, if the Earth was flat as our scientists are beginning to suspect how far away would the horizon be? or indeed would there be a horizon?
:rolleyes:

jimgriff
6th Jan 2009, 08:55
We ex mariners were taught that standing at the edge of the sea an average person (5'8") would see the horizon at 6.8 miles! :8

OFSO
6th Jan 2009, 08:56
I used to do the same thing sitting on my terrace on a clear winter's night in Darmstadt, Germany, watching aircraft heading south from FFaM. At a rough guess they were over Basel Switzerland when I lost sight, which would have been 300kms as a land track. I think that agrees mas o menos with other people's observations.

R

1DC
6th Jan 2009, 09:08
i have often wondered what the range of the strobe lights on a modern aircraft is. On a dark night with a clear atmosphere i see navigation lights flashing away from what seems to be a far off distance.What distance would you expect to see another aircraft's lights in these conditions..

Wholigan
6th Jan 2009, 09:17
Back of a cigarette packet calculation help

My word you gotta be some sort of posh bloke --------- 'twere always "back of a fag packet" when I were a lad. Unless, of course, you were being politically correct by trying not to use the word "fag".

:E;)

bnt
6th Jan 2009, 12:11
Are you people trying to say the Earth is round?:uhoh:
Hmmm, if the Earth was flat as our scientists are beginning to suspect how far away would the horizon be? or indeed would there be a horizon?
:rolleyes:
Some "scientists" they must be, if they can look across the sea, see that there is a horizon, yet still theorise that the Earth is flat. You rarely see such wilful dismissal of evidence outside "creation science", these days. :rolleyes:

Blacksheep
6th Jan 2009, 12:19
Back of envelope, 384.3 kmGood guess. That's roughly the range of a VHF Transceiver at 37,000 feet and VHF is limited by line of sight.

wondered what the range of the strobe lights on a modern aircraft isThat would depend on how powerful your telescope was... :suspect:

bnt
6th Jan 2009, 12:56
We ex mariners were taught that standing at the edge of the sea an average person (5'8") would see the horizon at 6.8 miles! :8
Well, if I plug those figures in, and say that your eyes are 1.7m, (about 5'7) off the ground, I work out that the horizon is only about 4.65km away. Stand on a foot-high box (0.3m higher, 2m total), and the horizon is just over 5.05 km away.

If you're watching a ship with a tall mast, however, it won't disappear over the horizon at such a distance. If it's a mast 30ft (10m) above the sea, the minimum horizon will be over 11km, more depending on how high you're viewing it from.

There's a lot more on horizons, including some nice graphics of the big triangle I was talking about, on this page: Distance to the Horizon &mdash; Steve Sque, University of Exeter (http://newton.ex.ac.uk/research/qsystems/people/sque/physics/horizon/)

Storminnorm
6th Jan 2009, 13:15
So why didn't those blokes on the Titanic see the iceberg?
( Apart from the fact it was night, and they had no headlights).

ALL boats should have headlights I reckon. :ok:

SpringHeeledJack
6th Jan 2009, 15:49
Thankyou gentlemen :D

I was standing on a small headland about 50m high, so my horizons were limited. I gave the height as 37,000ft as it might have been less, 34,000ft or perhaps more up to 41,000ft, so it seemed like a 'middle'... Generally what flight level would a west-bound transatlantic flight leave the coast of Ireland assuming that it originated in Europe ? Any ATCers here ?

I had always heard that the horizon was at around 12 miles, so using that formula earlier in the thread that would fit in with being on a commercial ship of sorts wouldn't it ?

My word you gotta be some sort of posh bloke --------- 'twere always "back of a fag packet" when I were a lad. Unless, of course, you were being politically correct by trying not to use the word "fag".

Well, I would've used the normal expression, but didn't want to push the envelope :p I wouldn't have used the term 'fag' on here, simply for the reason that an international readership might have been confused/abused/bemused by the term. An American friend wet themselves when shopping with me in the UK and found 'faggots in gravy' in the meat section some years back :}

I have watched the ISS orbit over my castle (well I am posh you know) in the last couple of years and have always tried to guess where it was directly above when passing out of my line of sight. It was generally several countries away by this point, at least that's what Jeeves explained whilst monitoring it on one's computer.

regards

SHJ

angels
6th Jan 2009, 16:13
SHJ - I once smuggled a pack of faggots into the States to prove to some friends that faggots were actually consumed in the UK.

They were made by Brains as well which added to the fun. :ok:

Checkboard
6th Jan 2009, 17:59
Kenny Everet used to do a joke about "Can I bum a fag?", as I recall.

Played "Nose Wheel Roulette" in Australia in my first airline as well. Job done with a stick of chalk, and required number of numbered lines drawn on sidewall of nose wheel. Most of the fleet ended up sporting chalked lines on the nose wheels :)

Beats "Autopilot Kerplunk", in that you lost less adrenaline, and stood the chance to make a few coins :ok: