The Helix

The Helix

A helix is the path of a point that rotates about an axis at constant speed while moving along that axis at constant speed. Screw threads, springs and spiral staircases are all helices.

The pitch is the distance advanced along the axis in one complete revolution — not the distance between adjacent plotted points.

Construction. Divide the plan circle into twelve equal parts and number them. Divide the pitch, marked on the elevation, into the same twelve equal parts. Point 1 in the plan projects up to height 1; point 2 to height 2; and so on. Join with a smooth curve. The result on the elevation is a sine curve, and its rise is uniform.

Hand. A right-hand helix advances away from you when turned clockwise — the standard for almost all threads. A left-hand helix does the opposite, and is used where rotation would loosen a normal thread. On a drawing the hand is visible in which way the curve leans, so it must be drawn correctly rather than sketched.

Worked example. A helix of 60 mm pitch divided into twelve gives 5 mm of rise per division. Dividing the circle into twelve but the pitch into eight gives a curve that is smooth, plausible and completely wrong — the two divisions must match.

Core checkpoint: Same number of divisions on the circle and on the pitch, and pair them in order.