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Parabolic Trough

5 min read

A parabolic trough is a curved mirror that focuses sunlight onto a pipe along its length and needs tracking in only one direction. Its concentration is the width of the opening divided by the circumference of the pipe, so a 1 m trough on a 5 cm pipe gives only 6.4x, while 30-80x needs a pipe of roughly 4 to 11 mm across. The mirror surface must be accurate to about 1.3° of slope for the light to land on a 5 cm pipe.

Part of Concentrating Optics

A parabolic trough is a mirror whose cross-section is a parabola, extended along its length, with a receiver pipe on the line where the sunlight converges.

The Shape And Its Numbers

A parabola of focal length f is y = x² ÷ (4f). Inputs, assumed for the example: opening width W = 1.0 m, focal length f = 0.4 m.

  1. Rim height above the vertex = (0.5)² ÷ (4 × 0.4) = 0.25 ÷ 1.6 = 0.156 m, about 16 cm.
  2. Distance from the rim to the focus = f + y = 0.4 + 0.156 = 0.556 m.

Make a template from this curve by plotting y for each x, cut ribs from plywood or sheet metal to it, space them along the length, and cover them with reflective sheet. The reflective sheet bends in one direction only, which suits a trough; a bowl needs segments.

Concentration Is Width Over Receiver Size

For a round pipe of diameter d, the receiver width the sunlight must fit onto is its circumference π × d, so the concentration C = W ÷ (π × d).

  • Pipe 5 cm (0.05 m): C = 1.0 ÷ (π × 0.05) = 6.4. With a 1.5 m opening, 9.5.
  • Pipe 2.5 cm: C = 12.7.
  • Pipe 1.27 cm (half inch): C = 25.
  • For C of 30-80 (the parent page’s range) on a 1 m opening: d = 1 ÷ (π × 80) = 4 mm up to 1 ÷ (π × 30) = 11 mm.

So the parent page’s 30-80x and its 5 cm pipe do not go together: a 5 cm pipe on a 1-3 m trough gives roughly 6-19x. A narrow pipe concentrates more but needs a better mirror and tighter tracking, because the light must land on a thinner target.

How Accurate Must The Surface Be?

By the law of reflection a surface tilted by an error ε sends its reflected ray off by 2ε. A ray off by 2ε travels a distance r to the pipe and lands 2ε × r away from the centre. For all rays to hit a pipe of radius 2.5 cm:

  • At the rim, r = 0.556 m, so ε ≤ 0.025 ÷ (2 × 0.556) = 0.0225 rad = 1.3°.
  • At the vertex, r = 0.4 m, so ε ≤ 0.025 ÷ (2 × 0.4) = 0.031 rad = 1.8°.

This ignores the sun’s own width (about 0.27° each side), which uses part of the allowance. For a 1 cm pipe the limit shrinks to about 0.5°. Check the template and the sheet’s shape against a straight edge.

What You Need

  • Plywood or sheet-metal ribs cut to the parabola
  • Reflective sheet — polished aluminium or mirror strips (Polished Sheet Metal)
  • A receiver pipe — blackened steel or copper, on supports at the focal line
  • A pivot so the trough rotates about its long axis
  • Water or oil circuit for the receiver

Method: Build And Aim

Step 1: Draw the parabola full size, make the template, cut at least three ribs.

Step 2: Join the ribs with stringers, bend the sheet over them and fix it without wrinkles.

Step 3: Set the pipe on the focal line with supports that do not shade the mirror.

Step 4: Aim: the trough’s shadow should fall evenly, or place a card at the pipe and watch the bright line sit on it.

Step 5: Track the sun by turning the trough about its long axis (Tracking Systems).

Common Mistakes

  • A 5 cm pipe expected to give 30-80x.
  • Sagging ribs. A sag of a few millimetres in a 1 m trough shifts the line off the pipe.
  • A pipe with no way to release pressure. Water in a sealed hot pipe is a boiler (Steam Generation).

Safety

A line of concentrated sunlight ignites and blinds

The focal line ignites wood, cloth and dry grass at once and burns skin; reflected glare at the ends and edges can reach eyes at a distance. Keep people and combustibles away from the focus and from the paths where it sweeps as the sun moves; cover the trough when not in use. Never look along the line. Eye injury from concentrated sunlight is permanent and painless.

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