Originally Posted by
Leisesturm
Your entire first paragraph is nonsensical and wrong. Hamilton is saying a lot of correct things in his posts, without using abstract geometric formulae and verbiage which just get in the way of what is rather simple physics.
H
I'm not sure if raising the stem will stretch the rider out further? But the original point was, I think, correct. The more leaned-forward the rider's torso is, the less the rider's CG moves rearward for a given raise of the handlebars.
As an extreme example, suppose the rider is initially in a completely flat back position, such that the line segment from his hips to his shoulder is parallel to the ground. His CG is roughly at his belly button. Then raise his hands a few inches. That raises the shoulder end of the line segment by a few inches, raises his CG by a couple inches, and moves his CG rearward by only a very small amount.
Attached below is a stick diagram illustrating this. Assume shoulder-to-hip distance 24 inch, start with shoulder-to-hip line horizontal (0 degrees), now raise shoulder 4 inch, the shoulder-to-hip line is now at 9.6 degrees, assume CG is on the shoulder-to-hip line 8 inches from hip, the CG is moved rearward by 0.1 inch.
This is just an approximation. In such a position, the CG is actually probably below his belly button (outside of the rider's body).
Of course, as the rider's initial position gets closer to fully upright, then raising the handlebar has a larger rearward effect on his CG position.