How to lay out a bolt circle by hand

What you are making

The worked example: a 300 flange with a 150 bore, eight 18 holes on a 240 bolt circle. The holes straddle the vertical and horizontal centre lines rather than sitting on them. The US Navy's machinery repairman manual explains why: on 4-, 8- and 12-hole flanges the holes straddle both centre lines so that a valve bolted to it sits truly vertical or horizontal, provided the holes of the pipe flange are in the standard places too — and it adds to check whether standard placement is wanted (NAVEDTRA 12204, p. 3-17).

Way one: dividers, set to the chord

The angle between neighbouring holes is 360° ÷ 8 = 45°. Stepping with dividers measures straight across, not round the curve, so set them to the chord between two holes, not to the arc: PCD × sin(180° ÷ number of holes) = 240 × sin 22.5° = 91.844. Mark the first hole on the bolt circle, then step the chord round from it; the eighth step should land back on the first mark. The Navy manual tabulates the same thing as a constant to multiply the pitch-circle diameter by (its 9-hole example: 0.342, which is sin 20°; NAVEDTRA 12204, pp. 3-19 to 3-20), and stepping a compass set to the chord round the circle is how Coey draws a regular polygon in a circle (Ch. 12).

Setting the dividers to the arc instead — the circumference divided by eight, π × 240 ÷ 8 = 94.248 — is 2.404 too long, and the eighth step lands about 20.86 round the circle past the first hole. The classic geometric division of a circle (Coey, Ch. 9) avoids the arithmetic but not the drawing error: whatever error the divider setting has is repeated at every step, so it adds up round the circle. Set from the computed chord, and correct the setting if the last step misses rather than spreading the error.

Way two: coordinates

On a mill, a drill with a readout or a layout table, mark each hole from the centre: x = r × cos θ, y = r × sin θ — the definitions of sine and cosine with the radius as the hypotenuse (FAA-H-8083-30B, p. 3-25) — with r the bolt-circle radius (120.00) and θ each hole's angle. Hole 1 at 22.5°: x = 120 × cos 22.5° = 110.866, y = 120 × sin 22.5° = 45.922.

Check before you drill

• Every pair of neighbouring hole centres should measure the chord, 91.844.
• Opposite holes should be one PCD apart, 240, through the centre.
• Material left between a hole and the outside edge: (300 − 240 − 18) ÷ 2 = 21.00; to the bore: (240 − 150 − 18) ÷ 2 = 36.00.

How this matches the tool

The bolt circle tool gives the same coordinates and chord for any number of holes and any clocking angle, checks the margins, and exports a DXF with centre lines. Every number on this page was produced by its own code when the page was built.

Sources

1. US Navy, Machinery Repairman 3 & 2, NAVEDTRA 12204 (1990), p. 3-17 “Laying Out Valve Flange Bolt Holes”: holes straddle both bisectors on 4-, 8- and 12-hole flanges
2. NAVEDTRA 12204 (1990), pp. 3-19 to 3-20, Table 3-2: pitch-circle diameter × constant = pitch chord
3. B. Coey, Pattern Development: Sheet Metal Level 1 (BCcampus, 2021, CC BY 4.0), Ch. 12 “Create Other Polygons”, p. 35: compass set to the side length, stepped round the circle
4. FAA-H-8083-30B, Aviation Maintenance Technician Handbook – General (2023), Ch. 3, p. 3-25: sine and cosine; public domain
5. Coey (2021), Ch. 9 “Divide a Circle into 12 Equal Parts”, p. 30