You are missing the fact that the head tube is angled. So, while angling the stem indeed shortens the reach as you drew, don't forget to consider the head tube angle when you run your projections.
I find the following calculator helpful when comparing stems:
http://www.habcycles.com/fitting.html
Thx, Trisk for posting that. I had found it searching TE and still couldn't wrap my mind aroud the math. I'm thick-skulled when it comes to math. I think, I almost get it...
OK, this set up I test rode was this:
70.1 HT angle (part that throws me-it's diff than avg basic example--he says you can add a calculation step to correct this)
120mm stem w/ 6 degree rise
51cm TT, but pushed back a wee bit... maybe 0.5cm, so TT 51.5cm effective
HT 110mm, no spacers underneath stem
The shop guy measured the drop of the bars to be about 1 inch below the saddle this way. My spine was pretty straight looking in the mirror, but it seemed a bit streched to the hoods on the trainer. When I got outside riding, it seemed better/shorter. Hmm.
Indysteele.... Thx... this makes more sense now. I have 2 Terry saddles in my "home collection" that I am going to re-try. I have wondered all along if a tri saddle might be good for me. I think part of my issue for saying this I found on TE. It was thread about ladies hormones changing and suddenly having saddle issues. My gyn doc says our tissues thin in times of perimenopause (like me). Too thick of chamois causes chaffing elsewhere for me I've found. So, if my body can make up the cushion diff, maybe a wee bit more cushion on the nose area (like tri saddles have) might be the right combo. After the correct fit of course.
Alpinerabbit... Thx for posting this pic! I'm a visual person and that seals the effect of the actual stem rise in my mind. I just need to finish what Trisk is telling me about the HT angle now...
This chart says it all:
http://www.habcycles.com/fitting.html