Screwballs,
I don't have Jeppesen available. In what context is 20 degs mentioned? One thing is what is used for procedure calculation, another thing is what you actually fly.
My calculation was meant as a practical example, and for sure I am using 30 degs AoB when needing to do a tight turn. Of course you are right, I took feet
pr. min and not
pr. second. Your calculation of approx 1500 meter for the radius is correct. Which just goes to show that it is not really possible to fly a circling in min visibility, especially if the MDH is higher than 600 and at high field elevation (higher TAS and hence GS). This emphasizes the need not to extent the downwind further than absolutely necessary.
My company recognized this problem by increasing our circling minima above the EU-OPS to 3000 meter met vis. It is still
very tight at some fields, with MDA of 1100 feet,
even if flying in landing configuration:
150 knot GS, 1100 feet for 33 seconds = 2546 meter
150 knot GS = 77 m/s, 30 deg AoB, radius = 1051 meter
150 knots GS is not unrealistically high for a 737-800, even in landing config flaps 40, if full of pax.
Max distance 3597 meter. BUT keep in mind that ICAO doesn't require you to keep the runway itself in sight, but runway
environment. That includes approach lights system or "or other markings identifiable with the runway". So technically it is possible, but tight... I would probably consider a diversion, depending on other weather factors (is it just mist and steady wind.. or heavy rain and gusty/turbulent), and I am quite sure no one would blame me afterwards.
As for in better conditions, I don't see a reason to extend the downwind, if you start the descent when beginning base turn, you have (in the above example) 2546 meter + 1/2 circumference to descent 1100 feet.
1/2 C = (pi x 2 x r) / 2 = 3300 meter
5846 meter = 3.15 nm ~ 3 degs path.

Also your downwind will already be extended further as you won't fly in landing config, hence your GS will be higher. Also you will have headwind (otherwise, why did you circle?). Plus you can adjust you AoB/fly the base a little further from the runway to give you more space..
There are other good reasons
not to extend, depending on the airport. Izmir, LTBJ, runway 34R circle to land 16L is a good example of that. Yes they do that at times in good weather conditions despite ILS16L available. If you extent your downwind you end up over a 1240 feet high hill (circling altitude 1500 feet).Being over it and unable to see it is more uncomfortable than starting the turn just prior, as it would work with 33 seconds (MD
H 1090 feet).
Like fighter pilots say (I was never one, but they have a lot of good sayings

), "fight like you trained, and train like you fight".