There also seem to be some theoretical issues, affecting how stress is distributed in the spring. It seems to me that there are three main issues. And, if I understand these correctly, they seem to imply that there is some minor mechanical advantage to the keeping the hook small.
In essence, the hook shape is designed so as to allow interaction with the cam foot of the tumbler, but there are some disadvantages and problems with it’s being there.
First, the hook changes the angle of pressure. As a result, a tremendous amount of torque is applied at the “L” bend and along the early part of the curve in the hook. Keeping the hook short is one way to keep that torque to a minimum. Making the hook longer is like adding a cheater bar to a wrench. With a wrench, adding length multiplies the amount of torque that “can” be applied. With the hook, adding length similarly multiplies the amount of torque that is applied at the “L”.
Note that it is not practical to simply make the hook a lot thicker and heavier than the neighboring leaf, in hopes of overcoming such stresses. If you make the back of the leaf (that is, the main bend area) of the spring thick, as it should be, and you make the hook overly thick, as you might do if trying to over-engineer the “L” and the hook, then you have put a weak spot in the spring just behind the “L”. In principle, the strength of the spring needs to taper consistently from the back toward the front. This helps distribute the load across its length evenly, without overstressing any particular point. And that’s why, from a theoretical perspective, the majority of better old locks have the thickness and width of the spring taper fairly consistently all the way down the leaf and continue to follow the same angle of taper on through the “L” and the curve of the hook. (As many of you have heard Hershel House say on his video, “Always taper when making a spring”.)
Second, the space available for the lower arm is a fixed variable in the geometry of any particular lock. The lower arm can’t be any longer than the space available between the forward lock nail and the tumbler. Total length of the lower arm is a combination of leaf plus hook. So a wide, open hook will in turn mean a shorter leaf section. The leaf section is the section best designed to flex, so it’s advantageous for it to be a long as possible. The longer it is, the more length there is over which to distribute the stress. Correspondingly, when working in conjunction with a long, well made leaf, a short tight hook is not required to carry so much of the load.
Third, the bend in the hook does not flex very well. Indeed, with such a bend, if it flexes much at all, it will break. So it is best if the majority of the flexing is done by the long, flat section of the lower arm, and as little as possible by the hook. For the reasons described above, keeping the hook as small as possible helps with this. A wide, open hook bears a lot of stress along its length.
Now, a final comment: In actual practice, the quality of the metal and temper may be more important than anything else in determining how well it actually functions and how long it lasts. What I’ve suggested above is all a matter of mechanical logic. The old guys who came up with superior lock designs did not have micrometers, high speed photography, etc., but they were talented engineers. Some of the details of the best locks show a very clear understanding of mechanical logic. We should not assume that it was all just trial and error.
