I have an old road bike with a quill stem and I want to raise the stem. After raising it to where I want it, the stem has about an inch between the high end of the expander nut and the top of the headset. I looked for markings on the stem and didn't see any indicating how much should be inserted. Is there a minimum amount that should be inserted into the headtube to ensure my safety?
I measured five quill stems that I have, three steel and two aluminum. The overall lengths vary from 5 1/2 to 6 1/4" (about 14 to 16 cm). The minimum insertion length was 2.5 to 3.0 inches (about 6.5 to 7.5 cm). There was not a consistant ratio of length to minimum insertion. It is possible that the insertion length increased on newer bikes due to safety/liability concerns. If you haven't got at least 2.5" (6.5cm) I would shop around for a longer quill or one that has an angled stem that will give you the height you need. An alternative is an adapter that inserts like a quilled stem but allows the use of threadless stems. The availability and variety of lengths and angles on modern stems will give you more options.
At a minimum, the entire "wedge" must be inside the tube. Beyond that, the wedge should be far enough away from the top of the tube that the force of the wedge (which is effectively trying to tear open the tube) will not be close enough to the tube end to split the tube end. I would put this latter distance at maybe 1.5", measured from the top of the wedge to the top of the tube.
Inserting more than that just doubles-up the stiffness of the two members, and reduces the length of the lever arm that would tend to bend things -- making for a stiffer/stronger setup, but no fundamental difference vs the roughly 1.5" insertion.