A Bushed Drilling Guide That Holds a Hand Drill Square: Angular Bounds, Hole-Position Error, and Bush Wear as the Limit

A hole drilled freehand is seldom perpendicular, and the resulting exit error grows with depth. This paper quantifies that problem for a stated unpractised user and designs a simple bushed guide block that bounds it. Freehand angular error is modelled as normally distributed with a standard deviation of 3.5 degrees: the mean absolute error is 2.793 degrees, the 90th-percentile absolute error is 5.757 degrees, and 56.77 percent of holes are off square by more than 2 degrees. At a depth of 50 mm the 90th-percentile hole-position error is 5.04 mm. A 25 mm thick guide block with a new diametral bush clearance of 0.15 mm bounds the angle to 0.344 degrees and the position error at 50 mm depth to 0.30 mm, a 16.8-fold reduction at the 90th percentile. That performance does not last. The clearance that corresponds to a 0.5-degree bound is only 0.218 mm and to a 1.0-degree bound only 0.436 mm. At a stated wear rate of 0.0030 mm per hole for a mild-steel bush, the 0.5-degree limit is reached after 22 holes and the 1.0-degree limit after 95 holes; a hardened bush at 0.00040 mm per hole reaches them after 170 and 715 holes respectively, and a polymer bush at 0.012 mm per hole after only 5 and 23 holes. The guide therefore works, but only as a wear-limited device: a soft bush is a short-lived consumable, not a permanent tool. A sizing rule is given: to hold a 0.5-degree bound at a worn clearance of 0.40 mm, the guide height must be at least 45.8 mm.