Screw flight calculator: the flat blank of a screw conveyor flight (auger), with the formula and a worked example

A screw conveyor flight, the auger, is a helicoid: a ribbon of plate wound round a pipe, rising one pitch per turn. Each turn is cut flat as a ring with a wedge missing and then opened out and pressed to the pitch. The whole layout comes down to four numbers -- the two radii of the ring and the angle of the wedge, from the two helix lengths -- and this page gives them for any flight, with the formula, a worked example and the forming notes that the formula does not tell.

The screw flight generator draws the blank, with the 1:1 template and the DXF for the plasma or laser table.

Screw flight calculator

Type the shaft, the flight outside diameter and the pitch: the calculator gives the two radii of the blank, the angle to cut out, both helix lengths and the weight of one turn.

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The dimensions

d is the inside diameter of the flight, which is the OUTSIDE diameter of the pipe or shaft it is welded to; D is the outside diameter of the flight; p is the pitch, the rise of the helix in one full turn, measured along the axis; t is the plate thickness, which does not change the blank but sets its weight and how it forms.

Standard pitch is equal to the flight diameter: a 200 mm screw has a 200 mm pitch. Half pitch is used on inclined screws and at the inlet of feeders, where the screw must not flood; long pitch, up to 1.5 D, for free-flowing material moved fast. Our example uses a long pitch, 250 mm on a 200 mm flight, because it shows the wedge clearly.

The hand: a right-hand flight, seen from the end, winds clockwise away from you, like a right-hand thread. Right hand is the default; the blank is the same for both hands -- what changes is the direction in which the two ends of the ring are opened.

The formula

Length of the two helices, one turn

Li = √((π × d)² + p²) ; Lo = √((π × D)² + p²) The inner edge of the flight follows the helix on the pipe and the outer edge the helix at the flight diameter; each is the hypotenuse of a circumference and a pitch.

Ring angle and radii

w = (D − d) / 2 ; ω = (Lo − Li) / w ; Ri = Li / ω ; Ro = Ri + w ω in radians is the part of the ring that STAYS; the wedge cut out is 360° − ω. The ring's inner arc measures Li and its outer arc Lo, which is the condition the shop checks.

Weight of one turn

weight = (ω / 2) × (Ro² − Ri²) × t × 7.85 / 10⁶ ω in radians, lengths in mm, 7.85 kg/dm³ for carbon steel. Multiply by the number of turns, which is the screw length divided by the pitch.

The helicoid is not developable: no flat plate lies on it without stretching. This blank gets both EDGES right, which is what the bench measures, and its area comes out a little over the finished flight -- 0.7 % in the example, up to 1.5 % on a wide flight. Forming takes that up. A blank larger than the finished flight is expected, not an error.

Worked example: a 200 mm flight on a 100 mm shaft, 250 mm pitch

The blank is a ring 246 mm across with a 73.1 mm hole and a 45.2° wedge taken out. Opened until the two cut ends stand one pitch apart along the axis, it becomes one turn of the flight.

Forming the flight

1. Cut the ring and the wedge: two concentric circles with Ri and Ro, and the two radii that bound the wedge of 360° − ω.
2. Clamp one cut end and pull the other along the axis until the gap between them is the pitch. Thin plate opens by hand or with a bar through the hole; thick plate goes to the press, in a pair of helical dies or between two bars set to the pitch.
3. Slide the turn over the pipe, set the pitch with a spacer or a gauge, and weld the inner edge to the pipe, one turn at a time, each butt-welded to the last. That is the sectional flight; the continuous helicoid flight is rolled from strip and is a different process.
4. Check the outer edge: it must measure Lo per turn and stand at D over the whole length. A flight that cups or wanders was opened unevenly.

Common mistakes

• Cutting ω out instead of the wedge. ω is what stays (314.8° in the example); the wedge to remove is 360° − ω.
• Using the pipe's inside diameter for d. The flight sits on the OUTSIDE of the pipe: d is the pipe outside diameter.
• Expecting the blank to lie flat on the finished flight. It cannot; the surplus area is what forming absorbs.
• Opening the ring the wrong way. Both hands come from the same blank; opening it the wrong way gives a left-hand flight, which conveys backwards.
• A pitch far larger than the diameter. Above about 1.5 D the flight is nearly straight, and above 10 D the calculation refuses it.

Frequently asked questions

How do I calculate a screw flight blank?

From the two helix lengths of one turn, Li = √((πd)² + p²) and Lo = √((πD)² + p²): the ring angle is ω = (Lo − Li) / w with w = (D − d) / 2, the inner radius Ri = Li / ω and the outer Ro = Ri + w. A 200 mm flight on a 100 mm shaft with 250 mm pitch: Ri = 73.1 mm, Ro = 123.1 mm, wedge 45.2°.

What is the standard pitch of a screw conveyor?

Equal to the screw diameter. Half pitch for inclined screws and feeder inlets, and up to 1.5 times the diameter for fast, free-flowing material.

Why is the blank bigger than the finished flight?

Because a helicoid is not developable: no flat plate lies on it without stretching. The blank matches both edges, and its extra area, under 1.5 %, is taken up when the ring is opened and pressed to the pitch.

How many blanks does a screw take?

One per turn: the length of the flighted part divided by the pitch. A 2 m screw at 250 mm pitch takes 8 turns, welded one to the next on the pipe.