Originally Posted by
mr_antares
Is this a Trig question?
The bar height will be length * sin(rise angle - 90). If you keep the angle the same, and shorten the stem, the bars will get lower.
I think that should be length * sin(rise angle - head tube angle) - if the stem angle is equal to the head tube angle, then the stem is horizontal and the height wouldn't change, and if the stem angles downward from the head tube to the bars then shortening the stem would actually raise the bars.
Remember to put your calculator into degrees mode before you do this - if you're not sure, take the sin of 90; if it's zero (or very close to zero) then you're in degrees, otherwise you're likely in radians!