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Accuracy & Focus Testing

4 min read

Test a concentrator with three measurements: find the focus with a white card, measure the smallest spot with a ruler to get the concentration ratio, and measure delivered power by heating a known mass of water, since power equals mass × 4.18 kJ/kg·K × temperature rise ÷ time. One kilogram of water warming 12 K in 60 seconds means about 840 W, and the whole test must be done with the target on a stick, never in your hand, because the focus of a 1.5 kW dish would put about 29 W through a human pupil.

Part of Building Reflectors from Salvage

Accuracy and focus testing is the set of simple measurements that show whether a built concentrator delivers the spot size and power it was designed for.

Three Measurements

Focus and spot size. Hold a piece of white paper or wood at increasing distances from the dish until the bright spot is smallest and brightest (parent page). Measure its width with a ruler; the parent page says a well-made dish gives a spot no larger than 2-5 cm. The concentration is dish area ÷ spot area. For a 1.5 m dish (1.77 m²) a 5 cm spot gives 1.77 ÷ 0.00196 = 900; a 10 cm spot, 1.77 ÷ 0.00785 = 225. The answer depends on how you define the spot’s edge, so measure it the same way each time.

Power. Put a known mass of water in a blackened can at the focus. The power delivered is mass × 4.18 kJ/kg·K × temperature rise ÷ time. Example: 1 kg of water rises by 12 K in 60 s: 1 × 4.18 × 12 = 50.2 kJ in 60 s = 0.84 kW, about 840 W. Compare it with the beam: 1.77 m² × 1,000 W/m² = 1,770 W, so the optical efficiency is 840 ÷ 1,770 = 47%, ignoring the heat the can loses. Use stirred water and a thermometer, and shorter runs so the can loses little heat.

Surface accuracy. A single tile throws a patch of its own width plus 0.0093 × its distance to the focus. If a tile 3 cm wide at 0.6 m gives a patch of 4.6 cm where 3.56 cm was expected, the excess of 1.0 cm is 2ε × 0.6 m, so ε = 0.01 ÷ 1.2 = 0.0083 rad = 0.48° of slope error across the tile (Mirror Tile Parabola derives the 3.56 cm).

Why The Test Is A Hazard

Take the parent page’s 1.8 m dish delivering 1.5 kW into a 5 cm spot. The flux is 1,500 ÷ (π × 0.025²) = 764,000 W/m². A pupil 7 mm across (area 3.85 × 10⁻⁵ m²) placed in the spot would admit 764,000 × 3.85 × 10⁻⁵ = 29 W. Looking straight at the sun admits 1,000 × 3.85 × 10⁻⁵ = 0.038 W, which is already harmful. The focus is about 760 times that. The retina has no pain sensors, so damage is not felt as it happens.

What You Need

  • A white card or board on a stick at least 1 m long
  • A ruler and a notebook
  • A blackened can, water, a thermometer and a watch
  • A cover for the dish
  • Eye protection for anyone near the focus

Method: Test Safely

Step 1: With the dish covered, set up the stick and card at the expected focus. Keep your head out of the cone between dish and focus.

Step 2: Uncover, read the spot, and re-cover. Do not leave it uncovered long.

Step 3: Run the calorimeter test in 60-second blocks, stir, read, and re-cover. Repeat several times and keep the best.

Step 4: Fix the weakest region first: re-aim misaligned tiles, repair a sagging rim, tighten the arm.

Step 5: Re-test at the hour you will use it, since the sun’s angle changes the focus slightly.

Common Mistakes

  • Testing by hand. The hand reaches the focus before the pain does.
  • A thin card that burns through. Use a thick board and watch it.
  • A cold can in a long test. Wind cools the can; shelter it.

Safety

The test target is the hazard: ignition, scalding, and permanent painless eye injury

The focus ignites cards and wood at once and can heat a litre of water to a scald within a few minutes. Concentrated sunlight at this power damages the retina permanently and painlessly. Keep the target on a stick, keep your face out of the cone and away from the focus, wear dark eye protection, and cover the dish between readings. A tracking concentrator left unattended sweeps its focus across whatever is near it.

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