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Thanks Frank on Fractals.
The Scillies helicopter ferry flew straight into the sea in 1986, killing 
several passengers. In certain light /sea state conditions, the eye cannot 
tell. I'm not sure if similar to Fractals, but result the same. That day, the 
 normal altimeter was inaccurate too. Only after that was automatic radar 
altimeter made compulsory on commercial helicopters!
Didn't Neil Armstrong manually fly the Apollo moon landing though? (CFIT). 
Maybe side lighting and shadows can overcome the fractal effect at certain 
angles?
Francis 

-----Original Message-----
From: NavList@fer3.com [mailto:NavList@fer3.com] On Behalf Of Frank Reed
Sent: 13 January 2019 23:16
To: francis@pharmout.co.uk
Subject: [NavList] Estimating distance on a Fractal World

A couple of days ago, the Chinese space agency released a  [LINK: 
https://www.youtube.com/watch?v=FbY887PwJeo] video taken by Chang'e 4 as it 
landed on the far side of the Moon. At first the spacecraft is flying 
horizontally, in orbit but rapidly reducing its forward velocity. By about 
0:40, you can see by looking at the distant craters that it is falling... By 
about 0:58, it is falling quickly, and the spacecraft then rotates to a 
vertical orientation to fire its rocket downward and land.
From about 1:10 onward, there's an interesting navigational problem. And it's 
a problem that will surely lead to a CFIT accident in the future if anyone is 
flying visually (CFIT="controlled flight into terrain" and implies that a 
pilot has flown into the ground without realizing that anything was wrong 
until impact or moments before). As you watch the ground coming up to you, 
notice that it looks nearly the same at every altitude, and you can't really 
guess when the spacecraft is about to set down! In mathematical terms, the 
surface is "fractal". It is self-similar at all scales. Or in simpler terms, 
there are small craters on the big craters, and little craters on the small 
craters, and even on the little craters there are tiny craters. It looks more 
or less the same at every scale. Ten miles above the ground looks about the 
same as a mile above the ground. A mile above the ground looks nearly the 
same as 500 feet above the ground.

Also, without an atmosphere, there is no extinction, no "blueing" of distant 
features. At every altitude, the surface appears crisp and sharp, as if it is 
right outside the window.

If you ever visit the Moon, be sure to bring radar (or sat nav), or you'll 
probably fly right into the lunar surface...

Frank Reed


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