I always favor bureaucratic cottages over some weak tile like silk. I have pondered iron many times, but still I prefer my cottage over it. I want an Oxford there soon.
Since both tiles are brown (1F1H), compare commerce:
Silk tile = 4C
Cottage = 1C (10 turns)
Hamlet = 2C (20 turns)
Village = 3C (40 turns) -- 4C with PP
Town = 4C -- 5C with PP -- 7C with FS+PP
It's been 16 turns since the last save... in the meantime you've grown from 13 -> 15, allowing you to work all of the new cottages AND the silk. Seeing your food surplus is +2 and you're at 43/50, I'll assume you've been size 15 for 9 turns (probably less).
By working the silk, you'd only delay the promotion of 1 cottage by 9 turns.
First 10 turns for silk:
+30C
Next 20 turns
+40C
I assume (again) that you might get PP before those 30 turns are done. So you're currently set back 70C (base).
A village with PP is worth the same as the silk tile... no loss here.
So you can only lose commerce for 9 turns (MAX) when the tile becomes a Town.
9 * (7-4) = 27C
Basically, you'd be
at least 53C ahead if you worked the silk tile over those crappy cottage tiles.
The silk is mightier than the cottage
Indeed. Duckweed was the first one who made me realize the strongest ratio is a 1 pop whip from size 2, giving something ~1.4 hammers per food w/o granary and 2.7 hammers/food with a granary.
Of course, 2 pop whips are preferable for less anger or 3 pop whips if necessary for big buildings like CHs or OR forges.
2 -> 1 pop whip is the strongest direct food to hammer conversion.
However, it's not necessarily the best setup.
For instance, consider that you have 2 corns and unlimited happiness... would you still do 2->1 whips? Of course not.
Basically, you have to look at this ratio:
(food surplus)/(food to grow)
Food to grow is easy. With a granary, it's 10 + pop at normal speed. Kinda like y = x + 10
If your food surplus increases with each population, you'll notice that
(food surplus)/(food to grow) tends to 1... in fact increasing your whipping potential, because you re-grow faster.
If it feels a bit strange, think of a city with only farmed 3F green tiles and no resources. Whipping becomes better at larger sizes. (you can whip more often)