Airspace and curvature

[neroliie]

Hello! I'm new here, this is my first post and so I hope you'll forgive any faux pas I make

I have a question which is likely quite silly, but I'll ask it anyway because it's been bugging me for a while and I'd rather I got an answer, even if it comes with some attitude

Wikipedia gives a definition of airspace as (paraphrased a bit) that portion of the atmosphere which is above a nation's territory and territorial waters. Presumably the boundaries between adjacent countries (eg Germany, Switzerland and Austria) then go upwards in a straight line perpendicular to the Earth's surface at that point.

In which case, given the curvature of the Earth, would it be true to say that at altitude a portion of airspace would be "wider" than the corresponding area on the ground? If so, does this have any consequences for air traffic, or is the planet's curvature so slight that the difference isn't worth considering?

[joelgarabedian]

Hi Neroliie,

It's a good question. The key is that the change in circumference is proportional to the relative change in radius. So if you have a circle of radius 1m, and increase the radius by a further 1m, the relative increase in circumference is much greater than having a circle with a radius of 100m, and increasing that by 1m. Given that the radius of the Earth is pretty large (6348km according to google), an increase in radius of, say 40000 feet (12.19km) has little effect on the overall circumference.

The radius of the Earth = 6348km
Circumference = 39885.6km

The radius of the Earth + 12.19km = 6360.19km
Circumference = 39962.25km

So the difference is just 76.7km - so 1km at sea level is equivalent to 1.0019km at 40000 feet.

Welcome to the forums

Joel.

[neroliie]

Joel, many thanks for your reply. It's clear to me now

[joelgarabedian]

Glad I helped

[LH2]

In which case, given the curvature of the Earth, would it be true to say that at altitude a portion of airspace would be "wider" than the corresponding area on the ground?

This has been answered, and as per the previous reply, you can see that this is of no practical consequence.

I was going to comment on another point, though, just for a bit of trivia:

then go upwards in a straight line perpendicular to the Earth's surface at that point.

Technically, if you defined airspace as the projection of a territory's boundaries along the vertical, and in turn you intuitively defined "vertical" as the direction of the local gravity vector (i.e., a plumb line), you would end up with a series of voids and overlaps in the ownership of airspace, as those "vertical lines" (which in reality are not even straight lines) would be crossing each other all the time. There is a simple solution to this which is to define "vertical" as a direction normal to a commonly agreed ellipsoid (such as could be GRS80), but again, since any voids and overlaps are in the order of a few metres at cruising altitudes this is also of no consequence.

Technically, if you committed an infringement just as you were passing through one of those airspace voids, and managed to get a very good geoscientist in your defence team, you could get away with it

[grizzled]

Welcome neroliie!

With that post you have managed something that many ppruners havent been able to do in years of posting: You asked a reasonable -- and interesting -- question and received exellent and interesting answers, with no flaming!

And what LH2 added is what often makes pprune such an interesting site. He/she has got us all thinking about other ramifications of your question -- be they "trivia" or not -- and therefore got us thinking out of the box.

So, at the risk (hope even?) that this thread will lead to an offshoot in JB, I will add to LH2's conjecture: In that same hypothetical court action, one could bring in a quantum physicist who would tell the court about the uncertainty principle. He would state that it is impossible, at any given instant to know both the velocity of the aircraft and it's position. So it could be shown that any evidence presented to show the aircraft was in spot "X" at time "y" is simply conjecture.

Case dismiised, I say.

Sorry neroliie, but this is what happens to interesting questions. And to further show you that it's not at all a silly question, I can tell you (from too many years of experience) that many controllers have spent many a midnight shift discussing your exact question amongst themselves.

grizz

[neroliie]

Hi LH2, thanks for your reply! I don't mind the trivia at all - in fact, when I was thinking about this before beginning the thread, the situation you describe was how I first formulated it - that is, with the voids in between different airspaces - if airspace were defined to have exactly the same dimensions irrespective of altitude. But I thought it wouldn't be too clear if I worded it like that.

Thanks for the welcome, grizzled I'd been lurking for a while before joining up. It's kind of intimidating when so many here seem to be in the industry and I'm just a fan girl

[Tim Zukas]

"those "vertical lines" (which in reality are not even straight lines) would be crossing each other all the time."

At the point where two "vertical" lines cross, gravity would be pulling in two different directions at once?