No immediate need for archery.
Axes are even better. Only reason to make archers instead is that they are cheaper. If you have to keep a large empire unfogged with units (because of raging barbarians setting), you need many units and can build 3 archers in time it takes to build 2 axe. If we don't need so many units, then axes are better because they make it possible to attack, not just defend (archers only good against barb axe if on hill or inside city in defense).
Do you know if we are playing with "Raging Barbarians" setting?
Do not whip axes in cities yet. If we are so unlucky that the barbs win all the battles, there is still time to whip after that.
Only need to put axe in queue in Gottingen, I think; and I would work the forested hill instead of the forested grassland, in order to ensure that we have enough hammers to whip the axe next turn if emergency.
One other thing... city specialization... do we have any? The most effective way to build an army is to build almost ALL the units in the most hammer-productive city (where you build barracks, forge, Heroic Epic, and not much else). Right now we could use CERN or Peri... but longer term I think Peri should be making cottages to specialize as commerce/science city, and CERN (capitol city) should become hybrid emphasizing both hammers and commerce (bureacracy civic will favor that). But for now, if we want to make fogbuster units or escorts for settlers or defense units, they should be made in CERN and Peri while other cities build infrastructure. The (maybe) whip in Gottingen is an emergency response to 2 barb axes and should not become routine.
We need a pure cottage city to drive science while we do ther things like build settlers or units. We also could benefit from setting up a GPFarm.
I know... I know... Rome was not built in a day....