OK, I did it. Two bikes, identical bars and stems.:
Atlantis, Brooks B-17, my fingertips were halfway between the stem and the bars.
Bridgestone, brooks woman's model with tiny nose, set up to fit the same as the atlantis, my fingertips did not reach the stem....
It seems like a really useful way of measuring, though, if you have a normal racing saddle.
Edit: Oh wait... I just reread your post and you said halfway up the stem.... so now I think I did it wrong... Are you saying that the elbow stays "hinged" and you basically see where your fingertips touch the bike, high-to-low? I was measuring more of a horizontal thing...
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