....The break gun uses a relatively big k with a relatively small x. The auto uses a relatively small k with a relatively big x....
I think what some of the folks were commenting about is the 'x' may be more similar than you're thinking. The travel of an internal side by side tumbler may not be too different than the swing on the hammer of an autoloader trigger group.
If the 'k' is much greater in the side by side their may be design, execution, etc. differences. Or, maybe the 'k' isn't too different.
