Aid for Drilling and Measuring Holes at Angle

This page provides a computational aid for drilling holes at angles and for measuring the angle of drilled holes. The intended application is for holes into the narrow sides of Pinewood Derby Car bodies. The bodies are required to have true bottoms and sides. The drilled holes are for attachment of single-wheel axles (nails) to the car. Sometimes one wants holes that are parallel to the bottom and perpendicular to the side of the car. One may also want holes that are at slight angles to the bottom and/or sides, called "camber" and "toe" respectively.

Drilling Holes at Angle

For drilling angled holes into the side of a thin car body, one needs a tool like a drill press with a flat, true horizontal surface and a true vertical surface, and a few calibrated spacers (drill bits) at small intervals. One needs also the proven ability to drill holes that are perpendicular to the flat, true horizontal surface to within a small fraction of a degree. This latter can be aided by using a drill guide attached to the top of the vertical reference surface and can be proven using the "Bracketing" measuring process elsewhere in this page.

Once the ability to drill true perpendicular holes is proven, the orientation of the workpiece can be adjusted relative to the two reference surfaces while the drill in the drill press chuck remains vertical. Workpiece orientation can be adjusted relative to the horizontal surface to produce "toe" (fore-aft orientation of the hole relative to perpendicular) and adjusted relative to the vertical surface to produce "camber" (top-bottom orientation).

Measuring Holes at Angle

For measuring, one needs a flat, true horizontal surface and a true vertical surface (if measuring holes in a thin car body), a machinist's square or try-square, a few calibrated spacers (drill bits) at small intervals, and an illuminated piece of white paper. The table of a drill press is usually adequate.

Two methods are offered: "Measurement at Parallel" and "Bracketing Parallel".

Measurement at Parallel

The general method is to offset the square and edge to be measured by a few inches and to sight between them, varying the angle of the square until the two edges appear parallel.

A technique for assessing "parallel" is to watch the space between the edges as the eye is moved left or right. At some angle the two seem to be almost together and then light disappears from between them. Parallel is when light disappears along the whole edge simultaneously.

The offered technique for varying and measuring the angle of the square involves placing two nearly identical known spacers (drill bits) between the heel of the square and the flat, true horizontal surface and measuring their separation. The angle of the blade relative to the surface can be calculated from the spacer sizes and separation using trigonometry.

Measurement by Bracketing Parallel

Once the square is aligned to indicate parallel to the angle of the edge being measures, the square may be rotated counterclockwise to find an arrangement of spacers and separation at which the "parallel" behavior just fails. Record these spacer and separation data in the "Low-side" column. Then rotate the square clockwise (High) through parallel until the "parallel" indication just fails again. Record these spacer and separation data in the "High-side" column. The javascript estimates the angle as midway between the low-side and high-side angles.

Computation Overview

The computational technique used in the page is "bidirectional", that is, it works from what is known (supplied by the user) and computes, if possible, what is not supplied. Computed results are identified using a ">" symbol ahead of the computed values. Some fields are "input only" and are indicated by the symbol "(R)" following the Variable name.