Quote of the Day

A wealth of information creates a poverty of attention.

— Herbert Simon, economist

This post will cover how to measure a countersink angle using gage balls. Figure 1 shows how a countersink is normally specified on an engineering drawing. I frequently use countersinks in my wood and metal working hobbies. In addition, using gage balls to measure the countersink angle provides a good example of how to apply basic geometry concepts to a practical problem. I use this example in my role as a volunteer adult math tutor at our local library.

Two gage balls of different diameters are used to measure the countersink angle (*θ*). Figure 2 shows the key variables involved: the diameter of ball 1 (*B _{1})*, the diameter of ball 2 (

*B*), and the height difference when placed into the countersink (

_{2}*M*). Figure 2 also presents the formula for the countersink angle

*θ*. The derivation requires only to apply the definition of the sine of a right triangle.

Figure 3 shows a scale drawing of a countersink angle measurement example.

Figure 4 shows how I performed the calculations in Mathcad.