<font color=blue>another factor comes to play in your formula</font color=blue>
Lots of factors indeed. That's why its just a rule of thumb. I've been on very hard 3 inch ice( even an inch and a half held me, barely, see above) and very weak 9-10 inch stuff. All depends on how it was formed. Snow makes for weaker ice, as does wind. The creepiest and strongest ice is the stuff that is totally clear, formed when no snow and no wind. I've only seen it once in my life. 10 inches thick and 22 degrees below zero F. No way to tell how thick it is with out drilling a hole. You can walk out on it, see the bottom, rocks, beer cans, tree stumps, weeds and you can't get near the fish. They see you coming and scatter. It's so clear you can't even see the ice. It is just like walking on water without getting wet. Very strange feeling.