Posted in 2023
Suppose a hole is drilled underground into the back of a drift. The hole is drilled from a pivot point at a particular height from the floor. Typically this height is a characteristic of the drill. In itself, this is relatively moderate and quite standard in underground mining. Sometimes, the drill may break down, and they need to use a different drill. Suppose further that the alternate drill has a different pivot height from the floor. How can we determine where the new pivot point of each hole would be without re-designing the pattern? To narrow the scope a little, how can we determine the new horizontal distance of the pivot point from the reference line?
I was working on some wage modelling in Excel and was looking at multiple increases within a given period. I wondered if the result of applying individual increases throughout the year is the same as applying the sum of the increases to the initial value (Spoiler: it is not). I work the algebra to satisfy my curiosity. It isn’t difficult, but it can be a mistake that is difficult to detect.