this post is really old, but just in case youre still wondering...
Here is the explanation I found in some thread somewhere. First the variables are explained, then the formulas, then examples... It helped me a lot to draw pictures to better understand what was happening. This is cut and pasted from an email to a friend... thats why the examples arent actually what you asked about...
SA = stem angle
--> e.g +/- 7deg = 83/97 degree
--> e.g. +/- 17deg = 73/107 degree
--> depends on whether the stem is "upside-down" or not.
--> can be measured if you have the right tools. or look it up online
HTA = head tube angle = determined by the frame of you bike, cannot be changed
--> a Trek 1500 in size 52 has a HTA of 71.5 degrees
--> a Lemond BA in size 55 has a HTA of 73.5 degrees
L = stem length = measured from center to center of clamps along the
side of the stem
Formulas:
(SA-HTA) = #
horizontal distance = COS(#)x(L)
verticle rise = SIN(#)x(L)
e.g.
(a)
--> 97deg - 71.5deg = 25.5deg
--> COS(25.5)(90mm) = 81.233mm
--> SIN(25.5)(90mm) = 38.746mm
(b)
--> 107deg - 71.5deg = 35.5deg
--> COS (35.5)x(110) = 89.553
--> SIN (35.5)x(110) = 63.877
(c)
--> 97deg - 71.5deg = 25.5deg
--> COS(25.5)(110mm) = 99.284mm
--> SIN(25.5)(110mm) = 47.356mm