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Parabolic Dish

4 min read

A parabolic dish is a bowl-shaped mirror that focuses sunlight onto a single point, giving the highest temperatures of any solar device but needing two-axis tracking and a small target. A 1.5 m dish with a 0.6 m focal length is about 23 cm deep and collects 1.77 m² of sun, so at a 60% optical efficiency it delivers roughly 1.1 kW to its focus, enough to melt aluminium in small amounts and braze copper.

Part of Concentrating Optics

A parabolic dish is a mirror shaped as a paraboloid, a parabola turned about its axis, so that all rays parallel to the axis meet at one point.

Geometry Of A Dish

The profile is z = r² ÷ (4f), where r is the distance from the axis and f the focal length. The depth at the rim of a dish of diameter D is D² ÷ (16 f).

Inputs, assumed: D = 1.5 m, f = 0.6 m (a focal-length-to-diameter ratio of 0.4, in the range of common dishes, recalled).

  1. Depth = 1.5² ÷ (16 × 0.6) = 2.25 ÷ 9.6 = 0.234 m, about 23 cm.
  2. Collecting area = π × 0.75² = 1.77 m².
  3. Sun power on that area = 1.77 × 1,000 W/m² = 1,770 W.
  4. At an optical efficiency of 60% (the parent page’s 1.8 m dish delivering 1.5 kW from 2.54 m² implies 1,500 ÷ 2,545 = 59%), delivered = 1,770 × 0.6 = 1,060 W, about 1.1 kW.

The efficiency is the product of mirror reflectance, the fraction of the dish actually covered by mirror, shading by the receiver, and surface accuracy. A tiled salvage dish loses much to gaps and slope errors (Mirror Tile Parabola).

Why A Dish Gets Hotter Than A Trough

A trough concentrates in one direction, so its ratio is the opening width over the pipe circumference. A dish concentrates in both directions, so the ratio is the dish area over the spot area. Dividing the 1.77 m² by a 5 cm spot (0.00196 m²) gives 900; by a 2 cm spot (0.000314 m²), 5,600. The parent page’s 100-1,000x is therefore a realistic range for tiled dishes whose spots are several centimetres across. What the spot temperature reaches is limited by radiation losses (Concentration Ratio & Temperature).

The price is tracking: the dish axis must point at the sun within a degree or two in both directions, all day (Tracking Systems), and the receiver must be small and tolerant of heat: a crucible, a pot, a steam boiler coil.

What You Need

  • A dish — a satellite dish (Satellite Dish Conversion) or a built frame
  • Reflective surface — mirror tiles or polished sheet
  • A sturdy receiver arm at the focal point
  • A two-axis mount with a lock
  • A cover for the dish and eye protection for the operator

Method: Check A Dish Before Using It

Step 1: Measure the dish diameter D and depth d, then compute f = D² ÷ (16 d). A dish that does not match the formula is not a true paraboloid (see offset dishes on the conversion page).

Step 2: Face the dish at the sun and hold a card at the computed focus; the bright spot should shrink to its smallest at that distance.

Step 3: Mount the target at the focus on a stiff arm that adjusts in and out.

Step 4: Lock the aim, then track every few minutes.

Common Mistakes

  • Measuring the focus from the rim instead of the vertex.
  • A thin, flexing receiver arm that wanders in the wind.
  • A target far smaller or far larger than the spot. A smaller target misses part of the light; a much larger one spreads the power over more surface and runs cooler than it could.

Safety

A point of intense heat and blinding light

At the focus of a 1 m² to 2 m² dish, wood ignites and metal melts; the beam burns clothes and skin, and the focus can reach well beyond the target when the dish is mis-aimed. Concentrated sunlight damages eyes permanently and painlessly: never look at the focus or at the mirror while it is aimed at the sun. A dish left unattended in the sun sweeps its focus across everything near it; cover it or turn it face down when you leave. In wind, stow it: even a modest wind loads a dish like a sail (Wind Loads).

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