New to the forum and this is my first time posting.

I have a 1990 trek 520 touring bike with a 19 inch frame. My wife wants to start riding this bike again after not doing so for many years. The problem with this bike is that the handlebars are pretty low in comparison to saddle height. They are about 2 inches lower than the seat when the stem is extended to it's maximum height. This is a pretty uncomfortable riding position for a road touring bike. I want to raise the bars about 2 inches, parallel to the seat, to make the ride more comfortable. I ordered a new stem ,which is substantially longer, that will let me raise the bars the additional height. I never raised handlebars this much before I was uncertain how much additional reach I should add to the stem to compensate for movement rearward along the headtube axis. By my calculations the handlebars will move rearward 17.5mm when the stem is raise 2 inches (the bike has a 71 degree head tube angle). My intuition says to order a stem with a 17.5mm longer reach. This would place the bars at the same distance forward from the seat except at a 2 inch higher height.

My question is: Is this the correct logic? I'm concerned that the rearward shift of the handlebars towards the seat is normal, and by design, of the bike designer. This rearward movement of the stem keeps the average rider in the proper comfortable position. It seems like a more upright riding position would require that the bars move closer to the saddle.

To the root of it all. Should I order a stem with a longer reach if I'm planning to raise the handlebars by this much???

I don't know if it matters but the current stem is 80mm long. It's angle appears to be the negative of the headtube angle.

Thanks for any helpful comments.