I keep looking for the answer to this question, but all I can find is the reverse: the need to move a saddle forward to maintain knee position after raising it. That is not what I am asking. I want to know how much do I have to raise my saddle after moving it forward (for whatever reason). I'm thinking the reach to the crank will have been shortened as the saddle moves more directly over it, not much but some. Anyone have a formula for this? I moved my saddle forward 1 cm.
I did a really quick and dirty approximation that suggests the amount the saddle has to be raised x is about y(cos theta) where y is how much I move the saddle forward and theta is the seat tube angle. Assuming 73 deg I get roughly 0.3 of the distance moved forward (or backward and lowering the saddle). So for my 1 cm change, I would need to raise the saddle about 3 mm. Not only is that a very small amount, but my seat post is stuck, so I will likely ignore it for now. At least until I decide if I like the new knee position. I know the saddle height will affect this, but I will work it out as I go.
Nevertheless, I would be interested in hearing what other folks come up with.