## Morris Dovey’s CNC Cove Radius Calculation |

Calculating the radius of a cove h units deep and w units wide
The equation of the line joining the midpoint of the arc to the right endpoint of that arc is given by: y = ((h / 2) / (w / 4)) * x y = ((4 * h) / (2 * w)) * x y = (2 * h / w) * x The slope of the line from the midpoint of the chord to the arc's center point is: m = -w / (2 * h) And so the equation of the line connecting the midpoint of the chord to the arc's center is: y = m * x + r; where r is the y-intercept (and the arc's radius!) Substituting at (w / 4, h / 2): (h / 2) = (-w / (2 * h)) * (w / 4) + r r = (h / 2) + (w / (2 * h)) * (w / 4) r = (h / 2) + (w * w) / (8 * h)
Determining the angular width of the coveWe can see that: tan A = (w / 2) / (r - h) = (w / (2 * (r - h))) So one-half of the angular width is given by A = arctan(w / (2 * (r - h))) And the entire angular width is simply 2 * A |