If many bottom-outs are happening, should air pressure or compression damping be increased? I know springs exert a force proportional to displacement from a steady-state position. On the other hand, an ideal damper exerts a force proportional to the speed of the object.

The procedure to tune an air fork that I have been taught is:


Set positive chamber air pressure according to a table with rider weights or by measuring sag.
Set compression damping according to current trail conditions each time. Aim for the least amount of damping which still avoids repetitive bottom-outs during the ride.


But I still struggle to understand why to increase compression damping instead of positive chamber pressure. What would be the difference?
Increasing positive chamber pressure would reduce bottom-outs, but at the expense of reduced "up" travel.  Increasing compression damping will also reduce bottom-outs but without reducing "up" travel.  This would have the negative effect of reducing the shock's compliance which will make the ride harsher, so it's a balancing act where the goal is to optimize the shock's action for the riding you do and how you want the shock to work for you.  If you mostly ride smooth trails but with occasional drops, then increasing positive chamber pressure so that you can keep compression damping low while still not bottoming out very often might work best.  If the shock is bottoming out every time you hit a big rock, then may you have to increase both positive chamber pressure and compression damping.

If you can't find an effective combo that doesn't reduce bottoming out, then maybe you need a longer-travel fork.