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I'm struck by the huge variations in the way that flight crews appear to programme their aeroplane to intercept the ILS..
If you offer me the opportunity to "self position", the chance I will "programme" the aircraft to do it is approz zero. I'll fly it myself thank you
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I've seen LLZ intercepts from 90 degrees to the LLZ and at ranges from
10 down to 5 nm from touchdown, even in very poor weather. I've seen aircraft whistle through the LLZ and (eventually) correct and some which clearly capture the GP from above
And I have seen all these from ATCOs

But more especially from pilots acting as Sim operators i.e. playing being an ATCO.
There is no "standard" way of doing it, and as pilots we are not trained in it. I am therefore not surprised at what you see - you have basically said to us "have a go yourself" and we are
Unless you now stipulate a range to be established, and depending on weather, I may essentially treat it as "a visual". 5NM might seem a good range to be established without checking further, and I may well not do an "intercept leg" as such.
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Personally, I have a strong professional wish to give the crew as stable an approach as possible
Appreciated... but weather dependant, and us now controlling ourselves, we only need to be stable by 1000' / 500'...
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Would you expect me to instruct you to go-round if I thought the approach was unstable, from what I observed on radar?
"Unstable" is hard to determine from radar - it essentially refers to speed and glideslope. Ordering a GA is a but drastic, but a subtle hint "confirm established" might be in order. I would not expect you to act as ZRH ATC and allow an aircraft to fly into a hill "because it was not your job"... However, I would expect you to lower your standards to those of safety, rather than expecting the intercept to meet your own standards