View Full Version : Perception Of Relative Altitude

Capt Pit Bull
4th Jul 2002, 02:53
I know many readers will know about this illusion, but I'd be willing to bet that not everyone does.

I offer this post by way of information for flight crew.

Everyone knows that cloud and haze layers can make it difficult to judge relative altitude. But some are not aware that even when the horizon is clearly defined, it is still extremely difficult to judge relative altitude, particularly at High Level

Why? Because the visual horizon is not in the same position as the local horizontal.

Draw the earth as a circle, then draw an aircraft exageratedly flying at altitude. Draw a line straight down from the aircraft to the centre of the earth.

Now draw another line, from the aircraft, tangental to the surface of the earth (i.e. just touching the edge of the circle).

Assuming that you have drawn this sufficiently exagerated, you should be able to see that the angle between the two lines is less than 90 degrees.

I.E. the visual horizon is not at right angles to the vertical, i.e. it is not horizontal.

If you know your geometry you can show that the angle between the visual horizon and the local horizontal is equal to the number of degrees around the circle that your tangent touches the circle.

In aviation terms, this means that however many degrees around the curvature of the earth you can see, the visual horizon will be depressed below the horizontal the same ammount.

So, say you are at cruising level, and it is a clear day such that you can see 120 Nautical miles. This equates to 2 degrees of arc. Hence, the visual horizon is depressed by 2 degrees.

How does this affect us?

So, if you were to see another aircraft at the same altitude as you, it would appear to be 2 degrees above the horizon, giving the impression that it was above you.
If you were making a vertical manoeuvre based on this perception, you'd probably choose to descend. Problem solved? Sadly not. Because the other crew see exactly the same thing. From their point of view, you also appear above the horizon, so a descent seems sensible. Now you're both descending, towards one another.

Take another example. Say an aircraft is 1,000' below you. It could appear to be above you, depending on its range. Using the 1 in 60 rule, 1,000 feet at 2 degrees gives us 30,000', or approx 5 miles.

Hence it would only appear below the horizon if it was at a range of less than 5 miles. At 5 miles it would be on the horizon. At more than 5 miles it would be above the horizon.

Again, a descent seems like a good idea. Sadly the traffic is below us.

What does this mean?

Even on a clear day, vertical manouevres based on visual spotting are a bad idea.

Don't use visual spotting to overrule TCAS, but if you are concerned about separation based on what you see, then supplement an RA with a turn.

Please note that the figures quoted abiove are a contrived round number example. Different altitudes will yield different angular and distance values.