how the ground track of a plane differs from what you appear to see from the ground

[wj9315]

Hi,
I've been watching the approach path of planes landing at heathrow, and comparing it to what's posted on the webtrak system.

I can't reconcile the two - the path of the webtrak system seems to show a path that is different by as much as 300 metres from the ground.

I've posted what I see from the ground vs. what the webtrak system shows:

Imgur: The most awesome images on the Internet (http://imgur.com/WLsCrt5)

essentially, the webtrak system shows a straight line, whereas what i see from the ground makes it look like the planes are in a completely different path. I understand that this must be some sort of optical illusion - does anyone have any material that allows you to calculate the groundtrack of an aircraft that you are observing in the sky from street level? Please let me know if there's any information i can provide to make this question clearer.

[Richard J.]

Estimating the ground track of an aircraft when viewing it from the ground is notoriously difficult. In relation to your map, where is your position on the ground, and what's the distance between you and the WebTrak path?

[DaveReidUK]

I've posted what I see from the ground vs. what the webtrak system shows

http://i.imgur.com/WLsCrt5.jpg

Assuming that the straight red track represents an aircraft on the localizer i.e. aligned with the runway heading, it's highly unlikely that you would observe another aircraft following the blue track, unless the pilot has had one too many. :O

WebTrak certainly has its faults (it sometimes misidentifies flights, or even fails to track them at all), but the tracks for those that it does plot are usually pretty accurate, as one would expect given that it's powered by NATS' radars.

[HEATHROW DIRECTOR]

From at least 8nm and much further out aircraft will be established on the ILS, as DR suggests. The final approach track is flown extremely accurately and will always be a straight line unless something untoward occurs.

[MarianA]

You need three pieces of information to fix the position of the aircraft you are seeing at a 3D-point for a given moment in time.

The following is not meant as practical exercise :-).

1) Azimuth.

Use a compass to get a bearing on your target.

You could draw a line on a map and know your target is somewhere above that line (or on it or even below it in the general case). So you have constrained position from anywhere in 3D-Space to one half of a 2D-plane.

2) Elevation.

Use a sextant to measure the angle from your eye between the horizon and your target.

Now you have removed another degree of freedom. You know your target is on a one-dimensional line. Extending from your eye, in the direction of the Azimuth and angled upwards at the elevation-angle.

For the third bit that finally constrains you to a zero-dimensional point in space you have a choice.

3a) Distance or "slant range".

Measure the apparent size of your airplane at unknown distance and the apparent size of a known object at a known distance. You could take a picture of the plane and put a ruler in it, or use a house that happens to be in it anyway. As you can also look up the actual size of the airplane you can calculate how far away it is along that slanted line.

You can convert elevation and slant range to find the distance on the ground and altitude. This is a bit of trigonometry. The slant range is the length of the hypothenuse in a right triangle where ground distance and altitude are the other two sides.

3b) Altitude.

Ask them for their altitude. I'd say you could use the data from the tracker, but as you are not trusting that it is not a real option for you.

If you do get an altitude (above or below your position), you know it will be along the slanted line at the point that happens to be at that altitude.

The math is about the same, only this time you know angle and length of the far leg of the triangle.

On a map you can now draw a point from you, in the direction of Azimuth, ground distance away, and label it with the altitude.

Do it quickly to sample several points, fit a nice path through them and you will find at that phase of flight it will be very close to a straight line for every successful landing. And also very close to the SAME straight line for different aircraft.

[Whoppa]

All is not how it seems. Using your sketch. Fold a right angle along the ground track. Get your eye down level with the paper and look at the sky track. It is curved, right? But you know that it is straight because it is above the ground track.

Stand on the sea front anywhere between the Isle of Wight and Swanage and look out to sea at the contrails of aircraft departing the UK to the South West. Many of the trails appear to show a right and then left turn. There is no change of direction, but a change of height as the aircraft leaves level flight and climbs to and reaches the next assigned altitude.