TRIVIA: The ILS glideslope GS is not exactly a straight line

[Alpha Floor 237]

You've ever thought that a glideslope of an ILS is a "straight" line in space from the Final Approach Point to the Touchdown Zone, right?

 

Well, it's not! At least not mathematically speaking

 

The reason why is simple: The GlideSlope emitter is not located on top of the runway for obvious reasons.

 

While the localizer antennas define a plane in space, the glideslope antennas define a very open, upside-down cone. The semi-angle of this cone is, for a standard 3 degree glidepath, 87º.

 

And the glideslope is the intersection of this cone with an offset plane that does not pass through the cone's vertex. Such intersection curve is called a HYPERBOLA

 

 

 

Image of a glideslope antenna (or set of antennas):

 

 

Image of a localizer antenna (or array of antennas):

 

Here's an image that "more or less" ilustrates the concept: 

 

 

So now you know. Next time somebody tells you an ILS is a straight line, you will now that ACTUALLY it's a HYPERBOLA. 

Be careful when you say this though, you might run out of friends, hahaha

[Murmur 3,941]

Great post Alpha Floor! I never thought about it. Appreciated the explanation. :smile:

[Alpha Floor 237]

Great post Alpha Floor! I never thought about it. Appreciated the explanation. :smile:

 

Thanks Murmur! Glad you enjoyed it!

[fs4fun 366]

Interesting, does the equipment in the aircraft correct for this? Otherwise the pilot could get the impression the aircraft is going to land short if they assume the glidepath is going to continue in a straight line instead of shallowing out.

[Alpha Floor 237]

Interesting, does the equipment in the aircraft correct for this? Otherwise the pilot could get the impression the aircraft is going to land short if they assume the glidepath is going to continue in a straight line instead of shallowing out.

 

Hi Barry!

 

I don't think the aircraft corrects for this, because it's not necessary. By the time the hyperbola becomes "curved" and stops being a good approximation of a straight line, the aircraft is already so close to the runway that visual references are used.

 

One thing that intrigues me, and I would ask a real pilot to confirm: Is the GLIDESLOPE indicating BELOW glidepath when the aircraft is on the runway and ABEAM the glideslope antennas? Theoretically, it should.

[bonchie 2,305]

By the time I'm touching down in real life, I'm always below the glideslope. I typically start to lose the glideslope about 50 above mostly because you don't drag a piston in nice and flat but instead head down and round out in the flare once you are visual. 

But a jet may show differently down to the runway.

 

Another thought about the shape of an ILS is that the further away you are, the less sensitive it is because like you said, it's not just a straight line shot into the sky. So if anyone has ever wondered why it's harder to hold an ILS on short final, that's why. 

 

This is different from an RNAV approach where the course guidance actually is a straight line and single point in space all the way down vs. being variable. 

[Murmur 3,941]

One thing that intrigues me, and I would ask a real pilot to confirm: Is the GLIDESLOPE indicating BELOW glidepath when the aircraft is on the runway and ABEAM the glideslope antennas? Theoretically, it should.

 

I tried it in X-Plane. The glideslope signal is lost if the aircraft is more than 40-45 degrees left or right of the glideslope (with reference to the ILS course). Don't know if this is realistic or not.

 

Apart from that, the effect you described is simulated: at constant altitude and horizontal distance (measured with respect to runway threshold), the glideslope indicator will show a different position, depending on the position of the aircraft with respect to the glideslope antenna.

Now that I think about it, this also explains why in every simulated landing I did, the glideslope indicator is always drifting upward (below the GS) in the final moments before flare and touchdown.

[Alpha Floor 237]

 

 

By the time I'm touching down in real life, I'm always below the glideslope. I typically start to lose the glideslope about 50 above mostly because you don't drag a piston in nice and flat but instead head down and round out in the flare once you are visual.

 

Thanks for confirmation! Yes, indeed once you fly over the threshold (or even way back), you're not paying any attention to the glideslope needle but flying visually instead

 

 

 

Another thought about the shape of an ILS is that the further away you are, the less sensitive it is because like you said, it's not just a straight line shot into the sky. So if anyone has ever wondered why it's harder to hold an ILS on short final, that's why. 

 

Hmmm, I'm not really sure that's the reason, i.e. that the hyperbola shape has anything to do with sensitivity. I believe localizer sensitivity has nothing to do with the glideslope at all

 

It's the same reason why a VOR radial get's more sensitive once you get closer to the station.

 

 

 

I tried it in X-Plane. The glideslope signal is lost if the aircraft is more than 40-45 degrees left or right of the glideslope (with reference to the ILS course). Don't know if this is realistic or not.

 

Thanks Murmur! I don't know it either.

[bonchie 2,305]

Hmmm, I'm not really sure that's the reason, i.e. that the hyperbola shape has anything to do with sensitivity. I believe localizer sensitivity has nothing to do with the glideslope at all

 

It's the same reason why a VOR radial get's more sensitive once you get closer to the station.

 

I wasn't talking about the glide slope. Just the localizer in general and it's shape going out.

 

Whether a glideslope gets less sensitive as you go out is a good question though. I've never payed much attention to it as I've always found a glide slope much easier to hold center then the LOC.

[Matthew Kane 1,343]

Does FSX or P3D simulate this or is it programmed in a straight line?

[Murmur 3,941]

Does FSX or P3D simulate this or is it programmed in a straight line?

 

Good question. I don't have them installed, but the fastest way to check would be this:

 

.) enter slew mode and move the aircraft to line it up with an ILS (both LOC and GS indicators centered, runway heading) at some distance from the runway;

.) keeping heading constant, slowly move the aircraft to the left. If the GS antenna is to the left of the runway, the GS needle should move down (towards an "above glideslope" position);

.) slowly move the aircraft to the right. The GS needle should move up (towards a "below glideslope" position);

.) if the GS antenna is to the right of the runway, the opposite should happen.

 

If nothing happens, then this phenomenon is not modeled.

[bonchie 2,305]

My guess would be that's a detail they probably didn't take the time to model, but who knows. These sims surprise me sometimes.

[Alpha Floor 237]

Good one Murmur!

 

I would try it on the runway threshold itself, aircraft on the ground. Slew to the side contrary to the GS antenna and the diamond should go up! Slew towards the antennad and diamond should go down!

 

If you're far out you won't notice anything, my guess.

[Jetstream96 20]

Good one Murmur!

 

I would try it on the runway threshold itself, aircraft on the ground. Slew to the side contrary to the GS antenna and the diamond should go up! Slew towards the antennad and diamond should go down!

 

If you're far out you won't notice anything, my guess.

Yes it does that in FSX, but only slightly noticeable when close to the runway. 

 

Actually it is quite straight forward mathematically. Deviating to the side making you father from the antenna, so you need to be higher in order to stay on the GS. i.e. (GS height) = (distance from antenna) * tan(3°)

[Dave Morgan 68]

Hi.

 

Rather enjoying stretching my spatial awareness and meagre maths by trying to define the hyperbola given only the glideslope angle and the glideslope beacon's distance from the runway. If the localiser plane is parallel to the GS cone's axis (I assume they are both vertical in practice) it's possible by rotating the cone's axial triangle... but the weather has finally improved so I'm out in the evenings and I have only an occasional 5 minute window at work. The simplest way is to use two right-angled triangles, one horizontal and one vertical.

 

Below is a nice illustration of the GS/LOC hyperbola, showing why you lose the GS shortly before landing. The GS beacon is the lamp, the LOC is the wall and the runway centreline is where the tabletop would meet the wall. A three degree GS that's offset by only a short distance from the runway would give near enough a straight line. Also, you could theoretically fly a neat go-around by following the back-course outwards but I guess the GS beacon doesn't cover the full 360°.

 

 

Best regards,

D