Stacked tolerances - or - How 0.006" made a difference

In going though normal everyday life six thousandths of an inch doesn't sound like a lot. But I just used that amount to fix a problem that I was having.I have a Hornady Lock-n-Load AP press to reload ammunition. In it I have installed a set of Redding dies to do the actual forming of the brass. But I had a problem.This only affected the first station of the press, but it annoyed the hell out of me. The first stage is to resize the brass and deprime it. The problem was the brass slightly canted outward and missed the "funnel" of the resizing die. (The reason it has a tight base is so it can resize the brass as far down as possible)With the brass slightly pointing outward (slight is maybe a degree or so) the mouth of the brass hit the flat outer part of the die and hung up. The tolerances of the shell plate allowing a bit of wobble and the small entry hole was the problem. Aggravating the issue was the circular spring that held the cases pressed lightly against the extractor notch on the head of the case that was forcing to to lean.Of course I could just nudge the case in a bit and then it would feed fine. But it's another thing to get me out of my rhythm. Getting out of rhythm when reloading is probably a bad things because you can make mistakes. Mistakes around ammunition are probably not a good thing. (!)I started to explore some possible solutions to the problem. My initial try was to mount something to push the mouth of the brass in -- emulating my finger. None of these worked for more than a cycle or two before they bent in a way that wouldn't do anything. The next option was to push the outside of the head (the bottom of the brass) up a bit.What to use?I fortunately have some feeler gauge stock that I used for my bike. 0.15mm for the intake and 0.30 for the exhaust valves. 0.15mm is 0.006 inches. Not much.Typically that thickness would be rounded to zero. In every day existence it's a non-event to have something be only that thick.I first pulled out my Dremel and ground a ramp onto the edges so as not to catch the cases as they fed on. I tried with both the 0.15 and 0.30 mm stock and no matter what I did to the thicker one it would still hang up. The 0.15mm worked fine without any problems. Again, 0.006" sounds like something small, but it's plenty thick to cause the case head to hang up.The difference in adding the 0.006" to the outside changed the angle enough to allow all of the cases to feed correctly through the sizing die!The tolerances between all the parts just added up a bit against me. Adding just six thousandths of an inch was enough to combat this.Afterward I sat down to do the math. How much difference did the added 0.006" make?I pulled out the micrometer and took some measurements:

(all measurements are in inches since that's the standard for most ammunition books)Then I started to do some trig:

...and...The added shim moved the end of the case 0.014". Just over a hundredth of an inch made all the difference![smugmug url="http://photos.vec.com/hack/feed.mg?Type=gallery&Data=14428733_BirdK&format=rss200" imagecount="100" start="1" num="100" thumbsize="Th" link="lightbox" captions="false" sort="true" window="true" smugmug="true" size="L"]