VIII. Compounding Errors

More often than not in our projects, no one part or measurement stands alone. Parts and measurements often build off of one another. An angle on this part should be mirrored on another it needs to interface precisely with or a dimension of one must reference another. For that reason, it is important to understand how errors in accuracy can stack or compound to create even larger errors.

If you’re a woodworker and familiar with table slaws and miter sleds, you may have heard of the 5 cut method for squaring your sled’s fence to the table saw blade. This method exploits the nature of compounding errors and with a little bit of math allows you to easily calculate the amount of required fence adjustment. The process works by making a normal 90 degree cut on a panel, rotating it 90 degrees and making another cut, and repeating until you’ve performed 5 cuts. If the fence and saw blade are truly set to exactly 90 degrees, you’ll end up with a piece that has all 90 degree corners as well. However, if the alignment is off even by a small amount, the amount of error in any single cut will be further magnified by each subsequent step, making it very obvious that something is wrong and there is a large visible error.

Another example, picture the humble picture frame with its four mitered corners. Now imagine instead of 45 degree angles, our saw is just a single degree out of alignment and we cut each angle to 44 degrees. When joining the two parts, what should have been a 90 degree angle has become 88 degrees. Repeat that for each of the next 3 corners and each will be affected by all of the prior, the error compounding and becoming more obvious at each step.

Therefore, it is important to understand not only the error tolerance of a single part on its own, but also to understand how the error relates and affects other parts it interfaces with.